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A strong convergence theorem on solving common solutions for generalized equilibrium problems and fixed-point problems in Banach space. (English) Zbl 1396.47004

Summary: In this paper, the common solution problem (P1) of generalized equilibrium problems for a system of inverse-strongly monotone mappings \(\{A_k\}^N_{k=1}\) and a system of bifunctions \(\{f_k\}^N_{k=1}\) satisfying certain conditions, and the common fixed-point problem (P2) for a family of uniformly quasi-\(\varphi\)-asymptotically nonexpansive and locally uniformly Lipschitz continuous or uniformly Hölder continuous mappings \(\{S_i\}^\infty_{i=1}\) are proposed. A new iterative sequence is constructed by using the generalized projection and hybrid method, and a strong convergence theorem is proved for approximating a common solution of (P1) and (P2) in Banach space.

MSC:

47J25 Iterative procedures involving nonlinear operators
47H10 Fixed-point theorems
47J20 Variational and other types of inequalities involving nonlinear operators (general)
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