Abstract
AbstractWe propose a modified hybrid projection algorithm to approximate a common fixed point of a "Equation missing"-strict pseudocontraction and of two sequences of nonexpansive mappings. We prove a strong convergence theorem of the proposed method and we obtain, as a particular case, approximation of solutions of systems of two equilibrium problems.
Highlights
We define an iterative method to approximate a common fixed point of a kstrict pseudocontraction and of two sequences of nonexpansive mappings generated by two sequences of firmly nonexpansive mappings and two nonlinear mappings
Let us recall from 1 that the k-strict pseudocontractions in Hilbert spaces were introduced by Browder and Petryshyn in 2
The reason, probably, is that the second term appearing in the previous definition impedes the convergence analysis for iterative algorithms used to find a fixed point of the k-strict pseudocontraction S
Summary
A Hybrid Projection Algorithm for Finding Solutions of Mixed Equilibrium Problem and Variational Inequality Problem. We propose a modified hybrid projection algorithm to approximate a common fixed point of a k-strict pseudocontraction and of two sequences of nonexpansive mappings. We prove a strong convergence theorem of the proposed method and we obtain, as a particular case, approximation of solutions of systems of two equilibrium problems
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