Existence of common fixed points using Bregman nonexpansive retracts and Bregman functions in Banach spaces

DOI10.1186/1687-1812-2013-113zbMath1423.47025OpenAlexW2135432726WikidataQ59292629 ScholiaQ59292629MaRDI QIDQ2249106

Nawab Hussain, Eskandar Naraghirad, Abdullah M. Alotaibi

Publication date: 8 July 2014

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

Full work available at URL: https://doi.org/10.1186/1687-1812-2013-113

zbMATH Keywords

reflexive Banach spaceBregman projectionBregman distanceBanach operator pairGâteaux differentiable functionBregman nonexpansive mapping

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

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Cites Work

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• Banach operator pairs and common fixed points in modular function spaces
• Fixed point and weak convergence theorems for point-dependent \(\lambda\)-hybrid mappings in Banach spaces
• Nonexpansive retracts and weak compatible pairs in metric spaces
• One-local retracts and Banach operator pairs in metric spaces
• Right Bregman nonexpansive operators in Banach spaces
• Banach operator pair and common fixed points for nonexpansive maps
• Asymptotically pseudocontractions, Banach operator pairs and best simultaneous approximations
• Fixed points, selections and common fixed points for nonexpansive-type mappings
• Banach operator pairs and common fixed points in hyperconvex metric spaces
• Fixed point theorems and convergence theorems for generalized nonspreading mappings in Banach spaces
• Common fixed points for Banach operator pairs with applications
• Two strong convergence theorems for Bregman strongly nonexpansive operators in reflexive Banach spaces
• Best simultaneous approximations, asymptotically nonexpansive mappings and variational inequalities in Banach spaces
• An iterative row-action method for interval convex programming
• Nonstandard methods in fixed point theory
• On the fixed points of commuting nonexpansive maps in hyperconvex spaces
• Iterative averaging of entropic projections for solving stochastic convex feasibility problems
• Totally convex functions for fixed points computation and infinite dimensional optimization
• \(q\)-hyperconvexity in quasipseudometric spaces and fixed point theorems
• Common fixed points for multimaps in metric spaces
• Common fixed points in best approximation for Banach operator pairs with Ćirić type \(I\)-contractions
• Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces
• Characterization of the subdifferentials of convex functions
• Common fixed points for commuting contraction mappings
• On the maximal monotonicity of subdifferential mappings
• Convergence Analysis of a Proximal-Like Minimization Algorithm Using Bregman Functions
• Monotone Operators and the Proximal Point Algorithm
• Construction of best Bregman approximations in reflexive Banach spaces
• Bregman Monotone Optimization Algorithms
• ESSENTIAL SMOOTHNESS, ESSENTIAL STRICT CONVEXITY, AND LEGENDRE FUNCTIONS IN BANACH SPACES
• One-local retract and common fixed point for commuting mappings in metric spaces
• NONEXPANSIVE NONLINEAR OPERATORS IN A BANACH SPACE
• On the Maximality of Sums of Nonlinear Monotone Operators

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