Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process

DOI10.1006/jmaa.1993.1309zbMath0895.47048OpenAlexW2086254189MaRDI QIDQ1310868

Kok-Keong Tan, Hong-Kun Xu

Publication date: 21 September 1998

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.1993.1309

zbMATH Keywords

nonexpansive mappingOpial's conditionconverge weakly to a fixed pointnorm is Fréchet differentiable

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

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pseudo-contraction mappings ⋮ Convergence theorems using Ishikawa iteration for finding common fixed points of demiclosed and 2-demiclosed mappings in Hilbert spaces ⋮ Strong convergence of a multiple-step iterative process for nonexpansive mappings ⋮ Approximate fixed points for nonexpansive and quasi-nonexpansive mappings in hyperspaces ⋮ Some weak convergence theorems for a family of asymptotically nonexpansive nonself mappings ⋮ Fixed points for mixed monotone multivalued operators in Banach spaces with applications ⋮ Strong convergence of an implicit iteration process for a finite family of generalized asymptotically quasi-nonexpansive maps ⋮ On \(\Delta\)-convergence theorems in CAT\((0)\) spaces ⋮ Weak convergence theorems for a countable family of Lipschitzian mappings ⋮ An accelerated common fixed point algorithm for a countable family of \(G\)-nonexpansive mappings with applications to image recovery ⋮ Convergence analysis of new construction explicit methods for solving equilibrium programming and fixed point problems ⋮ On solving pseudomonotone equilibrium problems via two new extragradient-type methods under convex constraints ⋮ On variational inequality, fixed point and generalized mixed equilibrium problems ⋮ On \(\triangle\)-convergence of iterative sequences in \(\operatorname{CAT}(0)\) spaces ⋮ Some observations on generalized non-expansive mappings with an application ⋮ Linear conditioning, weak sharpness and finite convergence for equilibrium problems ⋮ On the split equality fixed point problem of quasi-pseudo-contractive mappings without a priori knowledge of operator norms with applications ⋮ A strong convergence theorem for generalized-\( \varPhi \)-strongly monotone maps, with applications ⋮ A new modified three-step iteration method for G-nonexpansive mappings in Banach spaces with a graph ⋮ Novel self-adaptive algorithms for non-Lipschitz equilibrium problems with applications ⋮ Fixed point theorems for Lipschitzian type mappings in \(CAT(0)\) spaces ⋮ Strong and weak convergence of Ishikawa iterations for best proximity pairs ⋮ Studies on common solutions of a variational inequality and a fixed-point problem ⋮ Strong convergence of non-implicit iteration process with errors in Banach spaces ⋮ Some modified extragradient methods for solving split feasibility and fixed point problems ⋮ New semi-implicit midpoint rule for zero of monotone mappings in Banach spaces ⋮ Note on some results for asymptotically pseudocontractive mappings and asymptotically nonexpansive mappings ⋮ A new composite implicit iterative process for a finite family of nonexpansive mappings in Banach spaces ⋮ A new iterative algorithm for pseudomonotone equilibrium problem and a finite family of demicontractive mappings ⋮ Convergence of Mann's type iteration method for generalized asymptotically nonexpansive mappings ⋮ Halpern-type iterations for strongly relatively nonexpansive mappings in Banach spaces ⋮ Strong convergence theorems for a Mann-type iterative scheme for a family of Lipschitzian mappings ⋮ Hybrid inertial accelerated algorithms for split fixed point problems of demicontractive mappings and equilibrium problems ⋮ Convergence and weaker control conditions for hybrid iterative algorithms ⋮ Split feasibility and fixed-point problems for asymptotically quasi-nonexpansive mappings ⋮ Iterative method for approximating a common fixed point for family of multi-valued generalized hemi-contractive nonself mappings ⋮ Convergence of three-step iterations scheme for nonself asymptotically nonexpansive mappings ⋮ A Picard-Mann hybrid iterative process ⋮ Demiclosedness principle and approximation theorems for certain classes of multivalued mappings in Hilbert spaces ⋮ Mann and Ishikawa iterations with errors for asymptotically nonexpansive mappings ⋮ Weak and strong convergence theorems for mixed equilibrium problems in Banach spaces ⋮ Strong convergence of Mann's type iteration method for an infinite family of generalized asymptotically nonexpansive nonself mappings in Hilbert spaces ⋮ An application of proof mining to nonlinear iterations ⋮ Iterative methods of weak and strong convergence theorems for the split common solution of the feasibility problems, generalized equilibrium problems, and fixed point problems ⋮ On fixed point approach to equilibrium problem ⋮ Convergence of perturbed composite implicit iteration process for a finite family of asymptotically nonexpansive mappings ⋮ Strong convergence theorems for two total asymptotically nonexpansive nonself mappings in Banach spaces ⋮ Three-step Mann iterations for a general system of variational inequalities and an infinite family of nonexpansive mappings in Banach spaces ⋮ Weak and strong convergence theorems for a finite family of non-Lipschitzian nonself mappings in Banach spaces ⋮ Boundary point method and the Mann-Dotson algorithm for non-self mappings in Banach spaces ⋮ Convergence theorems of a new iteration for two nonexpansive mappings ⋮ Iterative sequence for asymptotically demicontractive maps in Banach spaces ⋮ Optimal parameter selections for a general Halpern iteration ⋮ On total asymptotically nonexpansive mappings in CAT(\(\kappa\)) spaces ⋮ Weak and strong convergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings ⋮ Strong convergence for asymptotically nonexpansive mappings in the intermediate sense ⋮ Demiclosed principle and convergence theorems for asymptotically strictly pseudononspreading mappings and mixed equilibrium problems ⋮ General composite implicit iteration process for a finite family of asymptotically pseudo-contractive mappings ⋮ The split common fixed point problem for asymptotically nonexpansive semigroups in Banach spaces ⋮ Implicit Ishikawa approximation methods for nonexpansive semigroups in CAT(0) spaces ⋮ An iterative shrinking metric \(f\)-projection method for finding a common fixed point of a closed and quasi-strict \(f\)-pseudocontraction and a countable family of firmly nonexpansive mappings and applications in Hilbert spaces ⋮ On the set of common fixed points of semigroups of nonlinear mappings in modular function spaces ⋮ Strong and \(\triangle\)-convergence theorems for two asymptotically nonexpansive mappings in the intermediate sense in \(\operatorname{CAT}(0)\) spaces ⋮ Weak convergence theorems for inverse-strongly skew-monotone operators and generalized mixed equilibrium problems in Banach spaces ⋮ On the iterates of asymptotically \(k\)-strict pseudocontractive mappings in Hilbert spaces with convergence analysis ⋮ Split common fixed point problem for quasi-pseudo-contractive mapping in Hilbert spaces ⋮ Non-expansive mappings and iterative methods in uniformly convex Banach spaces ⋮ Approximating fixed points of non-self nonexpansive mappings in Banach spaces ⋮ On convergence theorems for generalized alpha nonexpansive mappings in Banach spaces ⋮ The Krasnosel'skiĭ-Mann algorithm for a countable family of non-self Lipschitzian mappings ⋮ Existence and approximation of zeroes of monotone operators by solutions to nonhomogeneous difference inclusions ⋮ Generalized Krasnoselskii-Mann-type iteration for nonexpansive mappings in Banach spaces ⋮ Inertial relaxed \textit{CQ} algorithms for solving a split feasibility problem in Hilbert spaces ⋮ A new iteration technique for nonlinear operators as concerns convex programming and feasibility problems ⋮ Generalized mixed equilibrium problems and quasi-\(\phi\)-asymptotically nonexpansive multivalued mappings in Banach spaces ⋮ Approximating fixed points of \(\Phi\)-hemicontractive mappings by the Ishikawa iteration process with errors in uniformly smooth Banach spaces ⋮ Convergence of SP-iterations for generalized nonexpansive mappings in Banach spaces ⋮ Fixed point problems for nonexpansive mappings in bounded sets of Banach spaces ⋮ Strong and \(\varDelta\)-convergence of Ishikawa iterates of mixed type nonexpansive mappings in hyperbolic spaces ⋮ Alternating iterative algorithms for the split equality problem without prior knowledge of operator norms ⋮ The new extragradient method extended to equilibrium problems ⋮ Approximating common fixed points for a finite family of asymptotically nonexpansive mappings using iteration process with errors terms ⋮ Zeros of accretive operators and asymptotics of a second order difference inclusion in Banach spaces ⋮ Approximation of common fixed points of asymptotically nonexpansive cosine family based on modified Ishikawa iterations ⋮ Inertial extragradient algorithms for solving equilibrium problems ⋮ Approximating solutions of maximal monotone operators in Hilbert spaces ⋮ Weak and strong convergence results for solving inclusion problems and its applications ⋮ Hybrid implicit iteration process for a finite family of non-self-nonexpansive mappings in uniformly convex Banach spaces ⋮ Globally convergent diagonal Polak-Ribière-Polyak like algorithm for nonlinear equations ⋮ Iterative methods for generalized split feasibility problems in Hilbert spaces