A contribution to the theory of divergent sequences
From MaRDI portal
Publication:2647762
DOI10.1007/BF02393648zbMath0031.29501OpenAlexW2031685471MaRDI QIDQ2647762
Publication date: 1948
Published in: Acta Mathematica (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf02393648
Related Items
The subspace of almost convergent sequences ⋮ On the sublinear functional associated to a family of invariant means ⋮ Approximation of certain bivariate functions by almost Euler means of double Fourier series ⋮ On Browder's convergence theorem and Halpern iteration process for \(G\)-nonexpansive mappings in Hilbert spaces endowed with graphs ⋮ Dixmier traces and non-commutative analysis ⋮ Approximation of signals (functions) belonging to certain Lipschitz classes by almost Riesz means of its Fourier series ⋮ On ergodic operator means in Banach spaces ⋮ A note on \(F_ B\)-convergence ⋮ Lebesgue constants of the Walsh system and Banach limits ⋮ An abstract version of the Korovkin theorem via \(\mathcal{A}\)-summation process ⋮ Extremal properties of the set of vector-valued Banach limits ⋮ Finite-dimensional quasirepresentations of connected Lie groups and Mishchenko's conjecture ⋮ Generalized limits and statistical convergence ⋮ Some estimations of Banach limits ⋮ Singular approximation in polydiscs by summability process ⋮ Some \(\sigma\)-double sequence spaces defined by Orlicz function ⋮ Application of Banach limits to the study of sets of integers ⋮ On the structure of invariant Banach limits ⋮ \(\sigma\)-asymptotically lacunary statistical equivalent sequences ⋮ Strongly almost summable and strongly almost convergent sequences ⋮ On a new \(I\)-convergent double-sequence space ⋮ Convergence of positive linear approximation processes ⋮ Fourier-Stieltjes localization in neighborhoods of finite-dimensional irreducible representations of locally compact groups ⋮ Some spaces of double sequences obtained through invariant mean and related concepts ⋮ Domain of the double sequential band matrix \(B(\tilde{r}, \tilde{s})\) in the sequence space \(\ell(p)^\ast\) ⋮ Uniform mean convergence theorems for hybrid mappings in Hilbert spaces ⋮ Abstract Korovkin-type theorems in modular spaces and applications ⋮ On some new double sequence spaces defined by a modulus ⋮ Matrix transformations between the spaces of Cesàro sequences and invariant means ⋮ Domain of the double sequential band matrix in the classical sequence spaces ⋮ Some new sequence spaces derived by the domain of generalized difference matrix ⋮ Generalized limits with additional invariance properties and their applications to noncommutative geometry ⋮ On summability and positive linear operators ⋮ Almost \(\lambda_r\)-statistical and strongly almost \(\lambda_r\)-convergence of order \(\beta\) of sequences of fuzzy numbers ⋮ Banach limits and traces on \(\mathcal{L}_{1, \infty}\) ⋮ A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces ⋮ Weak convergence theorems for nonexpansive mappings in Banach spaces ⋮ Applications of double lacunary sequences to \(n\)-norm ⋮ Rate of convergence in \(L_p\) approximation ⋮ Lack of Tauberian theorem for absolute almost convergence ⋮ Structure properties of the Banach limit set ⋮ Characteristic functions of Banach limits ⋮ Quantitative theorems on linear approximation processes of convolution operators in Banach spaces ⋮ Durch Matrixverschiebungen erweiterte Konvergenzbegriffe ⋮ A note on some strongly sequence spaces ⋮ On the Riesz almost convergent sequences space ⋮ Invariant and absolute invariant means of double sequences ⋮ Some matrix transformations of convex and paranormed sequence spaces into the spaces of invariant means ⋮ On some lacunary almost convergent double sequence spaces and Banach limits ⋮ On infinite matrices and lacunary \(\sigma \)-convergence ⋮ Saturation of multiplier operators in Banach spaces ⋮ On \(\mathcal A\)-invariant mean and \(\mathcal A\)-almost convergence ⋮ An application of almost convergence in approximation theorems ⋮ \((A_\sigma)\)-double sequence spaces defined by Orlicz function and double statistical convergence ⋮ On vector-valued Banach limits ⋮ A note on \(\tau \)-convergence, \(\tau \)-convergent algebra and applications ⋮ Lebesgue constants of the Walsh system ⋮ Concerning Fatou's theorem ⋮ Dual convergence theorems for the infinite products of resolvents in Banach spaces ⋮ A Tauberian theorem related to almost convergence ⋮ Approximation theorems by positive linear operators in weighted spaces ⋮ A unified approach to the asymptotic almost-equivalence of evolution systems without Lipschitz conditions ⋮ Some variations of the Bohman-Korovkin theorem ⋮ On convergence of iterates of positive contractions in L\(_p\) spaces ⋮ On \(\sigma \)-conservative matrices and compact operators on the space \(V_{\sigma }\) ⋮ Almost convergence and generalized difference matrix ⋮ On almost \(p\)-bounded variation of lacunary sequences ⋮ On asymptotic formulae via summability ⋮ Dixmier traces as singular symmetric functionals and applications to measurable operators ⋮ On some generalized sequence spaces of fuzzy numbers defined by a sequence of Orlicz functions ⋮ On \(\sigma \)-conservative and boundedly \(\sigma \)-conservative four-dimensional matrices ⋮ Effective metastability of Halpern iterates in \(CAT(0)\) spaces ⋮ Invariant means on bounded vector-valued functions ⋮ Quantitative results on almost convergence of a sequence of positive linear operators ⋮ Invariant Banach limits and applications ⋮ Asymptotic almost-equivalence of Lipschitz evolution systems in Banach spaces ⋮ On the almost-convergence of iterates of a nonexpansive mapping in Hilbert space and the structure of the weak \(\omega\)-limit set ⋮ Strong and absolute almost-convergence of vector functions and related Tauberian theorems ⋮ Double sequence spaces characterized by lacunary sequences ⋮ Multidimensional matrix characterisations of the Banach and Pringsheim core ⋮ Fourier-Haar coefficients and Banach limits ⋮ Summation process of positive linear operators ⋮ Regularly \(\sigma \)-conservative and \(\sigma \)-coercive four dimensional matrices ⋮ Almost convergence and nonlinear ergodic theorems ⋮ On some new sequence spaces and statistical convergence methods for double sequences ⋮ Traces and residues of pseudo-differential operators on the torus ⋮ The set of almost convergent sequences as intersections of summability fields ⋮ Almost convergence and two matrix limitation methods ⋮ On generalized paranormed statistically convergent sequence spaces defined by Orlicz function ⋮ Zur Limitierung der beschränkten Folgen ⋮ On the invariant mean and statistical convergence ⋮ An application of medial limits to iterative functional equations ⋮ Tauberian conditions for almost convergence ⋮ Tauberian conditions for \(w\)-almost convergent double sequences ⋮ Almost convergence and Euler totient matrix ⋮ Generalized almost statistical convergence ⋮ Bound states and scattered states for contraction semigroups ⋮ A note on a mean ergodic theorem for nonlinear semigroups ⋮ Means on commutative semigroups and nonlinear ergodic theorems ⋮ Asymptotic behavior of solutions to nonlinear Volterra integral equations ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Summability of a Class of Fourier Series ⋮ A note on a theorem of Maddox on strong almost convergence ⋮ Unnamed Item ⋮ Some Sequence Spaces and Absolute Almost Convergence ⋮ A Sequence Space and Uniform $$(A,\varphi )$$—Statistical Convergence ⋮ Multiple disjointness and invariant measures on minimal distal flows ⋮ A nonlinear ergodic theorem for asymptotically nonexpansive mappings ⋮ Korovkin Type Approximation Theorem for Almost and Statistical Convergence ⋮ Invariant mean and a Korovkin-type approximation theorem ⋮ On some new matrix transformations ⋮ Asymptotic behavior of commutative semigroups of nonexpansive mappings in Banach spaces ⋮ On some difference sequence spaces defined by a sequence of Orlicz functions ⋮ Ergodic sequences of averages of group representations ⋮ On existence of finite invariant measures ⋮ Inäquivalenzsätze bei Limitierungsverfahren ⋮ Direct theorems on methods of summability. III. Absolute summability functions ⋮ An ergodic theorem for asymptotically nonexpansive mappings ⋮ Nonlinear ergodic theorems for commutative semigroups of asymptotically nonexpansive mappings ⋮ Almost statistical convergence of order \(\beta \) of sequences of fuzzy numbers ⋮ On strong almost convergence ⋮ Theorems of Toeplitz-Silverman type by applying a reduction method ⋮ On some spaces of almost lacunary convergent sequences derived by Riesz mean and weighted almost lacunary statistical convergence in a real \(n\)-normed space ⋮ Banach limits: invariance and functional characteristics ⋮ Some sequence spaces of invariant means and lacunary defined by a Musielak-Orlicz function over \(n\)-normed spaces ⋮ Summation Process by Max-Product Operators ⋮ Invariant Banach limits and their convex subsets ⋮ A new view at Dixmier traces on \(\mathfrak{L}_{1,\infty} (H)\) ⋮ On the difference spaces of almost convergent and strongly almost convergent double sequences ⋮ Banach limits and uniform almost summability ⋮ Further remarks on uniform statistical convergence of order \(\alpha\) ⋮ Order and geometric properties of the set of Banach limits ⋮ Some properties of the sequence space ⋮ Effective results on nonlinear ergodic averages in CAT spaces ⋮ Unnamed Item ⋮ Approximation theorems for functions of two variables via \(\sigma\)-convergence ⋮ Unnamed Item ⋮ New type of generalized difference sequence of fuzyy numbers involving lacunary sequences ⋮ Almost-convergent sequences with respect to polynomial hypergroups ⋮ Almost convergence and triple band matrix ⋮ Some properties of a function connecting to exponent of convergence for double sequences ⋮ Vector-valued almost convergence and classical properties in normed spaces ⋮ Matrix summability and positive linear operators ⋮ The method of almost convergence with operator of the form fractional order and applications ⋮ Viscosity Approximation Methods for Generalized Multi-Valued Nonexpansive Mappings with Applications ⋮ Advances in Dixmier traces and applications ⋮ Some topological properties of the spaces of almost null andalmost convergent double sequences ⋮ Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces ⋮ Characterization of ω -almost convergent sequences in Lp(T2) ⋮ The Nonlinear Ergodic Theorem for Asymptotically Nonexpansive Mappings in Banach Spaces ⋮ On some `duality' of the Nikodym property and the Hahn property ⋮ Almost convergence of double sequences and strong regularity of summability matrices ⋮ The space of almost convergent sequences ⋮ Unnamed Item ⋮ Nonlinear evolution equations and nonlinear ergodic theorems ⋮ Unnamed Item ⋮ On the Euler sequence spaces which include the spaces \(\ell _{p}\) and \(\ell _{\infty}\). II ⋮ The variances of a sequence ⋮ Infinite matrices and almost bounded sequences ⋮ Dual Convergences of Iteration Processes for Nonexpansive Mappings in Banach Spaces ⋮ Dixmier traces and extrapolation description of noncommutative Lorentz spaces ⋮ Lacunary Strong (A σ , p)-Convergence ⋮ A new type of convergence ⋮ On some generalizations of Lorentz's almost convergence ⋮ Almost-convergent double sequences ⋮ Consistency Theorems for Almost Convergence ⋮ Some new observations on Catalan almost convergent sequence spaces and the Catalan core ⋮ A strengthened form of a theorem of Wiener ⋮ Coefficient properties for certain Fourier series ⋮ Summability properties for the distribution of sequences ⋮ Banach limits, infinite matrices and sublinear functionals ⋮ On \(\sigma\)-finite invariant measures for Markov processes ⋮ Almost summable Taylor series ⋮ Matrix transformations of almost convergent sequences ⋮ Factor sequences for summability matrices ⋮ Some Topics in Summability Theory ⋮ Degree of Approximation of Functions Through Summability Methods ⋮ Negative Resultate über Tauber-Bedingungen ⋮ Strongly almost (ω, λ, q)-summable sequences ⋮ Weak mixing implies weak mixing of higher orders along tempered functions ⋮ A Class of Regular Matrices ⋮ An Application of Banach Limits ⋮ Infinite matrices and almost convergence ⋮ Toeplitz matrices, ergodicity and Fréchet spaces ⋮ Almost convergent vector sequences ⋮ Mean Values and Banach Limits ⋮ On the Hausdorff-limitability of \(\{ z^n\}\) ⋮ A study of the matrix method of summability of the trigonometrical series ⋮ Almost convergence in Banach spaces ⋮ A note on the \(\varepsilon\)-entropy of monotone functions in the Levy norm ⋮ On the lacunary partial sums of Walsh Fourier series ⋮ The Spectral Theory of Bounded Functions ⋮ The main classes of invariant Banach limits ⋮ On the degree of approximation of signals Lip(α,r), (r≥ 1) class by almost Riesz means of its Fourier series ⋮ Absolute summability functions for Hausdorff methods ⋮ Unnamed Item ⋮ Almost Convergence and the Buck-Pollard Property ⋮ Weighted means, generalised Hausdorff matrices and the borel property ⋮ A Note on the Ergodic Properties of Homeomorphisms ⋮ A Sufficient Condition for a Regular Matrix to Sum a Bounded Divergent Sequence ⋮ Matrix transformations and compact operators on the binomial sequence spaces ⋮ On the almost summability of a trigonometric sequence ⋮ On the ergodic theorem for positive operators I ⋮ ξ -Double Strongly Summable Sequences of order θ ⋮ Unnamed Item ⋮ On the summability of a sequence of Walsh functions ⋮ Banach and Statistical Cores of Bounded Sequences ⋮ On the Spaces of $\lambda _{r}$-almost Convergent and $\lambda _{r}$-almost Bounded Sequences ⋮ Positive linear operators and summability ⋮ On the Ergodic Mixing Theorem ⋮ Constant Functions and Left Invariant Means on Semigroups ⋮ On the Gamma Spaces Including the Spaces of Absolutely p-Summable, Null, Convergent and Bounded Sequences ⋮ Some new sequence spaces defined by bounded variation in 2-normed spaces ⋮ Lacunary almost convergence and some new sequence spaces ⋮ Almost Summable Sequences ⋮ On the K_{a}-continuity of real functions ⋮ Approximation by sampling type discrete operators ⋮ Mean ergodic type theorems ⋮ On strongly almost convergence of doubles equences via complex uncertain variable ⋮ Unnamed Item ⋮ Hausdorff dimension of the set of almost convergent sequences ⋮ Banach limits: extreme properties, invariance and the Fubini theorem ⋮ On the Range of an Invariant Mean ⋮ Almost Convergent and Almost Summable Sequences ⋮ 𝒜 $$\mathcal{A}$$ -Summability of Sequences of Linear Conservative Operators ⋮ Multivariate approximation in φ\varphi-variation for nonlinear integral operators via summability methods ⋮ Regular summability methods in the approximation by max-min operators ⋮ On uniform statistical convergence ⋮ Convergence of a conjugate function in Zygmund space by almost Nörlund transform ⋮ How large is the space of almost convergent sequences? ⋮ Hausdorff dimension of sets defined by almost convergent binary expansion sequences ⋮ Symmetric stable processes on amenable groups ⋮ A new paranormed sequence space and invariant means ⋮ Almost convergent sequence spaces derived by the domain of quadruple band matrix ⋮ Asymptotic behavior of a periodic sequence of nonexpansive mappings with applications ⋮ Almost convergent \(0\)-\(1\)-sequences and primes ⋮ Domain of the Cesàro mean of order α in Maddox’s space ℓ(p) ⋮ Riesz I-convergent sequence spaces ⋮ A General Korovkin Result Under Generalized Convergence ⋮ On a mixing property of operators in Lp spaces ⋮ On invariant measures for operators ⋮ Summability in Amenable Semigroups ⋮ Geometry of Banach limits and their applications ⋮ A relation of Banach limit and difference matrix to generate some Orlicz sequence spaces ⋮ Summability on Mellin-type nonlinear integral operators ⋮ Invariant Banach limits and their extreme points ⋮ On Nonstrongly Regular Matrices ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Consistency theory for SM-methods ⋮ Ergodic properties of operators in some semi-Hilbertian spaces ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Weighted Statistical Relative Invariant Mean in Modular Function Spaces with Related approximation Results ⋮ On a new I-convergent sequence space ⋮ Unnamed Item ⋮ Consistency theory for SM-methods ⋮ Characterization of Absolute and Uniform Continuity ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Weak almost-convergence theorem without Opial's condition ⋮ Finitely additive measures on \(\mathbb{N}\) ⋮ Infinite Matrices and Invariant Means ⋮ On some sequence spaces ⋮ Some new sequence spaces defined by lacunary sequences ⋮ Order Summability and Almost Convergence ⋮ Characterization of Cesàro andL-asymptotic limits of matrices ⋮ Multipliers for the Space of Almost-Convergent Functions on a Semigroup ⋮ The existence of non-trivial bounded functionals implies the Hahn-Banach extension theorem ⋮ Strong asymptotic behavior of almost-orbits of nonlinear semigroups ⋮ An ergodic theorem for nonlinear semigroups of Lipschitzian mappings in Banach spaces ⋮ Unnamed Item ⋮ A direct approach to positive normalised traces on simply generated ideals ⋮ Variational principles for spectral radius of weighted endomorphisms of 𝐶(𝑋,𝐷) ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Complementarity of subspaces of ℓ_∞ revisited ⋮ I2-lacunary strongly summability for multidimensional measurable functions ⋮ Nonexpansive retractions and nonlinear ergodic theorems in Banach spaces ⋮ Unnamed Item ⋮ On the asymptotic behaviour of almost-orbits of nonlinear contraction semigroups in Banach spaces ⋮ Quadratic inequalities for functionals in l^{∞} ⋮ A survey on some paranormed sequence spaces ⋮ Unnamed Item ⋮ Multidimensional Strongly Deferred Invariant Convergence ⋮ On the ergodic theorem for positive operators I ⋮ Statistical σ-convergence of double sequences with application ⋮ Lacunary sequences of complex uncertain variables defined by Orlicz functions ⋮ A-statistical convergence of order α via φ - function ⋮ Almost λ-Statistical Convergence of Complex Uncertain Sequences ⋮ Strongly \((V_{\sigma},\lambda,q)\)-summable sequences defined by Orlicz functions ⋮ The \(\sigma\)-convergence and \(\sigma\)-core of double sequences ⋮ On lacunary \(\sigma\)-statistical convergence ⋮ Reproducing kernels and skew-dilation of Hilbert space operators ⋮ On lacunary invariant sequence spaces defined by a sequence of modulus functions ⋮ Distribution of values of bounded generalized polynomials ⋮ On domain of Nörlund matrix ⋮ Extreme points of the set of Banach limits ⋮ Connes-Dixmier traces, singular symmetric functionals, and the notion of Connes measurable element ⋮ Approximation processes with respect to positive multiplication operators ⋮ Almost lacunary statistical and strongly almost lacunary convergence of sequences of fuzzy numbers ⋮ Uniform distribution, invariant means, and Riemann integrals ⋮ Generalized difference strongly summable sequence spaces of fuzzy real numbers defined by ideal convergence and Orlicz function ⋮ \(r\)-convex sequences and matrix transformations ⋮ Applications of Orlicz-Pettis theorem in vector valued multiplier spaces of generalized weighted mean fractional difference operators ⋮ \(K_a\)-convergence and Korovkin type approximation ⋮ Asymptotic behavior of solutions to the semidiscrete diffusion equation ⋮ A summability process on Baskakov-type approximation ⋮ Generalized matrix summability of a conjugate derived Fourier series ⋮ Statistical convergence of double sequences in locally solid Riesz spaces ⋮ Spaces of strongly lacunary invariant summable sequences ⋮ Double almost lacunary statistical convergence of order \(\alpha\) ⋮ On some new sequence spaces defined by infinite matrix and modulus ⋮ Generalized weighted invariant mean based on fractional difference operator with applications to approximation theorems for functions of two variables ⋮ A note on double lacunary statistical \(\sigma\)-convergence of fuzzy numbers ⋮ Generalized limits and sequence of matrices ⋮ On almost \(B\)-summable double sequence spaces ⋮ Weighted almost convergence and related infinite matrices ⋮ Domain of the Nörlund matrix in some of Maddox's spaces ⋮ Double almost statistical convergence of order \(\alpha\) ⋮ Dilation invariant Banach limits ⋮ A generalization of almost convergence ⋮ Extreme points of the set of dilation-invariant Banach limits ⋮ Sequential definitions of continuity for real functions. ⋮ Almost periodicity and ergodic theorems for nonexpansive mappings and semigroups in Hadamard spaces ⋮ Convergence in phi-variation and rate of approximation for nonlinear integral operators using summability process ⋮ Generalized almost convergence and core theorems of double sequences ⋮ \(\sigma\)-core and \(\mathcal I\)-core of bounded sequences. ⋮ Almost conservative four-dimensional matrices through de la Vallée-Poussin mean ⋮ Compact operators for almost conservative and strongly conservative matrices ⋮ Some new classes of generalized difference strongly summable \(n\)-normed sequence spaces defined by ideal convergence and Orlicz function ⋮ Vector valued Banach limits and generalizations applied to the inhomogeneous Cauchy equation ⋮ Generalized statistically almost convergence based on the difference operator which includes the \((p,q)\)-gamma function and related approximation theorems ⋮ Continuity conditions for finite-dimensional locally bounded representations of connected locally compact groups ⋮ Domain of Riesz mean in some spaces of double sequences ⋮ Some seminormed difference sequence spaces over \(n\)-normed spaces defined by a Musielak-Orlicz function of order \((\alpha, \beta)\) ⋮ Approximating fixed points for a reversible semigroup of Lipschitzian mappings in a smooth Banach space ⋮ Statistical \(\mathcal{A}\)-summation process and Korovkin type approximation theorem on modular spaces ⋮ On generalized sequence spaces via modulus function ⋮ Almost convergence and generalized weighted mean. II ⋮ Vector valued multiplier spaces of \(f_\lambda \)-summability, completeness through \(c_0(X)\)-multiplier convergence and continuity and compactness of summing operators ⋮ On paranorm \(\mathrm{BV}_\sigma\) \(I\)-convergent double sequence spaces defined by an Orlicz function ⋮ On the domain of the triangle \(A(\lambda)\) on the spaces of null, convergent, and bounded sequences ⋮ Summability process by Mastroianni operators and their generalizations ⋮ The spaces of \(B(r,s,t,u)\) strongly almost convergent double sequences and matrix transformations ⋮ \( \lambda \)-almost summable spaces ⋮ Statistical relative \(\mathcal{A}\)-summation process and Korovkin-type approximation theorem on modular spaces ⋮ Nonlinear approximation in \(N\)-dimension with the help of summability methods ⋮ Operator valued series, almost summability of vector valued multipliers and (weak) compactness of summing operator ⋮ A new RH-regular matrix derived by Jordan's function and its domains on some double sequence spaces ⋮ On subsets of the space of bounded sequences ⋮ Banach limits: some new thoughts and perspectives ⋮ Tauberian conditions for almost convergence in a geodesic metric space ⋮ The order of approximation by positive linear operators ⋮ Banach limits and a measure on the set of 0-1-sequences ⋮ Wijsman lacunary \(\mathcal{I}\)-invariant convergence of sequences of sets ⋮ On the degree of approximation of functions in a weighted Lipschitz class by almost matrix summability method ⋮ An axiomatic approach to complete patience and time invariance ⋮ On the factorable spaces of absolutely \(p\)-summable, null, convergent, and bounded sequences ⋮ On the space of almost convergent sequences ⋮ \(f\)-asymptotically lacunary ideal equivalence of double sequences ⋮ Weak almost periodicity and the strong ergodic limit theorem for contraction semigroups ⋮ Relative weighted almost convergence based on fractional-order difference operator in multivariate modular function spaces ⋮ Strongly almost lacunary \(I\)-convergent sequences ⋮ Almost sequence spaces derived by the domain of the matrix \(A^r\) ⋮ Optimal simultaneous approximation via \(\mathcal{A}\)-summability ⋮ Power boundedness and similarity to contractions for some perturbations of isometries ⋮ Almost strongly regular matrices and a core theorem for double sequences ⋮ Almost convergence and a core theorem for double sequences ⋮ General methods of convergence and summability ⋮ Almost absolute weighted summability with index \(k\) and matrix transformations ⋮ Independent sequences, monotonicity of Banach limits and applications to noncommutative geometry ⋮ Invariant linear functionals on \(L^\infty(\mathbb{R}_+)\) ⋮ A mean ergodic theorem for nonlinear semigroups which are asymptotically nonexpansive in the intermediate sense ⋮ Summation of almost convergent divergent sequences, topological methods ⋮ A generalization of almost convergence, completeness of some normed spaces with wuC series and a version of Orlicz-Pettis theorem ⋮ Translation-invariant linear forms on C\(_0\)(G), C(G), L\(^p\)(G) for noncompact groups ⋮ \(P\)-statistical summation process of sequences of convolution operators ⋮ On the characterization of some classes of four-dimensional matrices and almost \(B\)-summable double sequences ⋮ On Fourier-Haar coefficients of the function from the Marcinkiewicz space ⋮ Criteria of regularity for norm-sequences ⋮ Weak convergence theorems for asymptotically nonexpansive mappings and semigroups ⋮ Convergences of nonexpansive iteration processes in Banach spaces ⋮ Spaces of \(A_\lambda\)-almost null and \(A_\lambda\)-almost convergent sequences ⋮ Approximation of functions by the sequence of integral operators ⋮ On some classical properties of normed spaces via generalized vector valued almost convergence ⋮ Comments on the paper Weak almost-convergence theorem without Opial's condition ⋮ Order properties of the set of Banach limits ⋮ On Banach-Mazur limits ⋮ Banach limit, fixed points and Ulam stability