Modified Halpern's iteration for fixed point theory of a finite family of \(G\)-nonexpansive mappings endowed with graph

DOI10.1007/S13398-017-0390-YOpenAlexW2601601111MaRDI QIDQ1742916

Atid Kangtunyakarn

Publication date: 12 April 2018

Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13398-017-0390-y

zbMATH Keywords

dominating set\(G\)-nonexpansive mapping\(G\)-\(S\)-mapping

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69)

Related Items (6)

Convergence of a new three-step iteration process to common fixed points of three \(G\)-nonexpansive mappings in Banach spaces with directed graphs ⋮ On a fixed point theorem with application to functional equations ⋮ Unnamed Item ⋮ Generalized rational contractions in semi metric spaces via iterated function system ⋮ A regularization method for solving the G-variational inequality problem and fixed-point problems in Hilbert spaces endowed with graphs ⋮ Unnamed Item

Cites Work

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• Fixed point theory for nonlinear mappings in Banach spaces and applications
• On Browder's convergence theorem and Halpern iteration process for \(G\)-nonexpansive mappings in Hilbert spaces endowed with graphs
• Attractive points and Halpern-type strong convergence theorems in Hilbert spaces
• Convergence analysis of a monotone projection algorithm in reflexive Banach spaces
• Hybrid iterative scheme for generalized equilibrium problems and fixed point problems of finite family of nonexpansive mappings
• Weak and strong convergence theorems for nonspreading mappings in Hilbert spaces
• Approximation of fixed points of nonexpansive mappings
• Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces
• Strong convergence of the composite Halpern iteration
• Strong convergence of hybrid Halpern processes in a Banach space
• The contraction principle for mappings on a metric space with a graph
• Fixed points of nonexpanding maps

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