Strong convergence for countable generalized Bregman nonexpansive-type mappings with equilibrium and variational inequality constraints

2026/08/05 by Markjoe O. Uba
Mathematics · #math.FA #msc:47H09 #msc:47H10 #msc:47J25 #msc:47J20 #msc:65K15

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arxiv created 2026/08/05 · arxiv updated 2026/08/06

Abstract

We develop a Legendre--Bregman outer-approximation method for a common-solution problem in a uniformly smooth and uniformly convex Banach space. The constraint system consists of countable families of fixed-point-type mappings, equilibrium bifunctions, and monotone variational-inequality operators. Strong convergence to the Bregman projection of the initial point onto the common solution set is obtained without a family-level NST compatibility condition. A localized theorem covers negative-entropy generators, and Hilbert-space and Alber-functional cases are also derived.

Citations

• Perturbation-resilient inertial Krasnosel'skii-type hybrid retractions for generalized nonexpansive mappings
• A hybrid scheme for fixed points of a countable family of generalized nonexpansive-type maps and finite families of variational inequality and equilibrium problems, with applications
• Metric and Generalized Projection Operators in Banach Spaces: Properties and Applications
• The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming