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A hybrid approximation method for equilibrium and fixed point problems for a family of infinitely nonexpansive mappings and a monotone mapping. (English) Zbl 1223.47071

Summary: We introduce a new iterative scheme for finding a common element of the set of fixed points of a family of infinitely nonexpansive mappings, the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for an \(\alpha\)-inverse-strongly monotone mapping in the framework of a Hilbert space. Under suitable conditions, some strong convergence theorems for approximating a common element of the above three sets are obtained. Additionally, we utilize our results to study the optimization problem and find a zero of a maximal monotone operator and a strictly pseudocontractive mapping in a real Hilbert space. Our results improve and extend the results announced by many others.

MSC:

47J25 Iterative procedures involving nonlinear operators
47H10 Fixed-point theorems
49J40 Variational inequalities
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