A unified theory of cone metric spaces and its applications to the fixed point theory

DOI10.1186/1687-1812-2013-103zbMath1294.54035arXiv1111.4920OpenAlexW2096605837WikidataQ59292829 ScholiaQ59292829MaRDI QIDQ2249116

Petko D. Proinov

Publication date: 8 July 2014

Published in: Fixed Point Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.4920

zbMATH Keywords

fixed pointsBanach contraction principlePicard iterationcone metric spaceiterated contraction principlesolid vector space

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Fixed-point and coincidence theorems (topological aspects) (54H25) Numerical solutions to equations with nonlinear operators (65J15) Other ``topological linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than (mathbb{R}), etc.) (46A19) Ordered topological structures (06F30)

Related Items (32)

Semilocal convergence of Chebyshev-like root-finding method for simultaneous approximation of polynomial zeros ⋮ Convergence of Newton, Halley and Chebyshev iterative methods as methods for simultaneous determination of multiple polynomial zeros ⋮ Approximation of point of coincidence and common fixed points of quasi-contraction mappings using the Jungck iteration scheme ⋮ Ascoli-type theorems in the cone metric space setting ⋮ A unified semilocal convergence analysis of a family of iterative algorithms for computing all zeros of a polynomial simultaneously ⋮ Convergence of relaxed minimizers in set optimization ⋮ Relevant classes of weakly Picard operators ⋮ Some remarks on Perov type mappings in cone metric spaces ⋮ Extension procedures for lattice Lipschitz operators on Euclidean spaces ⋮ On the convergence of Schröder's method for the simultaneous computation of polynomial zeros of unknown multiplicity ⋮ Best proximity point for q-ordered proximal contraction in noncommutative Banach spaces ⋮ Common fixed points of weak contractions in cone metric spaces ⋮ Fixed points and endpoints of set-valued contractions in cone metric spaces ⋮ Fixed point theorems in quaternion-valued metric spaces ⋮ A general semilocal convergence theorem for simultaneous methods for polynomial zeros and its applications to Ehrlich's and Dochev-Byrnev's methods ⋮ On a family of Weierstrass-type root-finding methods with accelerated convergence ⋮ Unified convergence analysis for Picard iteration in \(n\)-dimensional vector spaces ⋮ A fixed point approach to the stability of functional equations on noncommutative spaces ⋮ Abstract theorems on exchange of limits and preservation of (semi)continuity of functions and measures in the filter convergence setting ⋮ Iterative approximation of fixed points of quasi-contraction mappings in cone metric spaces ⋮ On the convergence of Gander's type family of iterative methods for simultaneous approximation of polynomial zeros ⋮ General convergence theorems for iterative processes and applications to the Weierstrass root-finding method ⋮ The Relevance of a Metric Condition on a Pair of Operators in Common Fixed Point Theory ⋮ Algebraic structures for pairwise comparison matrices: consistency, social choices and Arrow's theorem ⋮ Perov-type contractions ⋮ The method of searching for zeros of functionals on a conic metric space and its stability issues ⋮ Various generalizations of metric spaces and fixed point theorems ⋮ Fixed point theory of cyclic operators ⋮ On the equivalence between Perov fixed point theorem and Banach contraction principle ⋮ Best proximity points in noncommutative Banach spaces ⋮ On the convergence of high-order Ehrlich-type iterative methods for approximating all zeros of a polynomial simultaneously ⋮ A convergence analysis of a fourth-order method for computing all zeros of a polynomial simultaneously

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