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Generalized mixed equilibrium problem in Banach spaces. (English) Zbl 1178.47051
From the summary: This paper uses a hybrid algorithm to find a common element of the set of solutions to a generalized mixed equilibrium problem, the set of solutions to variational inequality problems, and the set of common fixed points for a finite family of quasi-$\varphi$-nonexpansive mappings in a uniformly smooth and strictly convex Banach space. As applications, we utilize our results to study an optimization problem.

47J25Iterative procedures (nonlinear operator equations)
47H09Mappings defined by “shrinking” properties
47H05Monotone operators (with respect to duality) and generalizations
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
47J20Inequalities involving nonlinear operators
Full Text: DOI
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[9] Matsushita, S. and Takahashi, W. Weak and strong convergence theorems for relatively nonexpansive mappings in Banach spaces. Fixed Point Theory Appl. 67(6), 37--47 (2004) · Zbl 1088.47054 · doi:10.1155/S1687182004310089
[10] Nilsrakoo, W. and Saejung, S. Strong convergence to common fixed points of countable relatively quasi-nonexpansive mappings. Fixed Point Theory Appl. 2008, Article ID 312454, 19 pages (2008) DOI: 10.1155/2008/312454 · Zbl 1203.47061
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