A new fixed point technique for equilibrium problem with a finite family of multivalued quasi-nonexpansive mappings

Sow, T.M.M.

doi:10.2478/gm-2022-0009

Abstract

We introduce a new iterative scheme by viscosity approximation method for finding a common point of the set of solutions of an equilibrium problem and the set of common fixed points of a finite family of multivalued quasi-nonexpansive mapping in a Hilbert space. It is proved that the sequence generated by the iterative scheme converges strongly to a common point of the set of solutions of an equilibrium problem and the set of common fixed points of a finite family of multivalued quasi-nonexpansive. Futhermore, we applied our main result for finding a common solution of convex minimization problem and fixed points problem. Essentially a new approach for finding solutions of equilibrium problems and fixed point problems whith set-valued operators is provided.

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A new fixed point technique for equilibrium problem with a finite family of multivalued quasi-nonexpansive mappings

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