Abstract
In this paper, we prove strong convergence theorem for finding a common element of the set of fixed point of a finite family of nonexpansive mappings and a finite family of -strictly pseudocontractive mappings and the set of a finite family of the set of solution of equilibrium problems by using the new mapping generated by a finite family of nonexpansive mappings and a finite family of -strictly pseudocontractive mappings and a sequences of positive real numbers. Furthermore, by using our main result, we obtain two interesting theorems involving variational inequality problems and variational inclusion problems. In the last section, we give numerical examples to support our main results.
Highlights
Let H be a real Hilbert space and C be a nonempty closed convex subset of H
Question Can we prove a strong convergence theorem for finding a common solution of the set of fixed point of a finite family of nonexpansive mappings and a finite family of strictly pseudocontractive mappings and a finite family of the set of solution of equilibrium problems?
In this paper, motivated by the ongoing research and Theorems . and . , we prove strong convergence theorem for finding a common solution of the set of fixed point of a finite family of nonexpansive mappings and a finite family of strictly pseudocontractive mappings and a finite family of the set of solution of equilibrium problems by using the mapping defined by ( . )
Summary
Let H be a real Hilbert space and C be a nonempty closed convex subset of H. We prove strong convergence theorem for finding a common solution of the set of fixed point of a finite family of nonexpansive mappings and a finite family of strictly pseudocontractive mappings and a finite family of the set of solution of equilibrium problems by using the mapping defined by
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