Strong convergence theorems for equilibrium problems and weak Bregman relatively nonexpansive mappings in Banach spaces

DOI10.1186/1029-242X-2013-119zbMath1471.47042WikidataQ59301621 ScholiaQ59301621MaRDI QIDQ2636689

Yeol Je Cho, Ravi P. Agarwal, Jia-wei Chen

Publication date: 31 January 2014

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

zbMATH Keywords

fixed pointequilibrium problemBregman projectionBregman distanceLegendre functiontotally convex functionshrinking projection algorithmweak Bregman relatively nonexpansive mapping

Mathematics Subject Classification ID

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

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Cites Work

• Algorithms of common solutions for variational inclusions, mixed equilibrium problems and fixed point problems
• Systems of generalized nonlinear variational inequalities and its projection methods
• Two strong convergence theorems for Bregman strongly nonexpansive operators in reflexive Banach spaces
• Levitin-Polyak well-posedness by perturbations for systems of set-valued vector quasi-equilibrium problems
• An Inexact Hybrid Generalized Proximal Point Algorithm and Some New Results on the Theory of Bregman Functions
• Iterative Methods for Solving Systems of Variational Inequalities in Reflexive Banach Spaces
• Two Strong Convergence Theorems for a Proximal Method in Reflexive Banach Spaces
• Proximal Minimization Methods with Generalized Bregman Functions
• Construction of best Bregman approximations in reflexive Banach spaces
• Bregman Monotone Optimization Algorithms
• ESSENTIAL SMOOTHNESS, ESSENTIAL STRICT CONVEXITY, AND LEGENDRE FUNCTIONS IN BANACH SPACES
• Nonlinear Proximal Point Algorithms Using Bregman Functions, with Applications to Convex Programming

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