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A modified hybrid projection method for solving generalized mixed equilibrium problems and fixed point problems in Banach spaces. (English) Zbl 1232.47049
Summary: We introduce a modified new hybrid projection method for finding the set of solutions of generalized mixed equilibrium problems and convex feasibility problems for an infinite family of closed and uniformly quasi-\(\varphi \)-asymptotically nonexpansive mappings. Strong convergence theorems are established in a uniformly smooth and strictly convex Banach space which also displays the Kadec-Klee property.

MSC:
47J25 Iterative procedures involving nonlinear operators
47J20 Variational and other types of inequalities involving nonlinear operators (general)
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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