Abstract
Abstract In this paper, we introduce an iterative scheme for finding a common element of the sets of fixed points for multivalued nonexpansive mappings, strict pseudo-contractive mappings and the set of solutions of an equilibrium problem for a pseudomonotone, Lipschitz-type continuous bifunctions. We prove the strong convergence of the sequence, generated by the proposed scheme, to the solution of the variational inequality. Our results generalize and improve some known results. MSC:47H10, 65K10, 65K15, 90C25.
Highlights
In, Browder and Petryshyn [ ] introduced a concept of strict pseudo-contractive in a real Hilbert space
Note that the class of strictly pseudo-contractive mappings strictly includes the class of nonexpansive mappings, which are the mappings T on C such that
In the recent years, iterative algorithms for finding a common element of the set of solutions of equilibrium problem and the set of fixed points of nonexpansive mappings in a real Hilbert space have been studied by many authors
Summary
In , Browder and Petryshyn [ ] introduced a concept of strict pseudo-contractive in a real Hilbert space. In the recent years, iterative algorithms for finding a common element of the set of solutions of equilibrium problem and the set of fixed points of nonexpansive mappings in a real Hilbert space have been studied by many authors (see, e.g., [ – ]).
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