Abstract
In this paper, we construct a new hybrid projection method for approximating a common element of the set of zeroes of a finite family of maximal monotone operators and the set of common solutions to a system of generalized equilibrium problems in a uniformly smooth and strictly convex Banach space. We prove strong convergence theorems of the algorithm to a common element of these two sets. As application, we also apply our results to find common solutions of variational inequalities and zeroes of maximal monotone operators.
Highlights
Let E be a Banach space with the norm · and let E* denote the dual space of E
Motivated by the results of Shehu [ ], we prove some strong convergence theorems for finding a common zero of a finite family of continuous monotone mappings and a solution of the system of generalized equilibrium problems in a uniformly smooth and strictly convex real Banach space with the Kadec-Klee property
Let C be a closed convex subset of a smooth strictly convex and reflexive Banach space E and let f be a bifunction from C × C to R satisfying the conditions (A )
Summary
Let E be a Banach space with the norm · and let E* denote the dual space of E. Kohasaka and Takahashi [ ] proved that if E is a smooth strictly convex and reflexive Banach space and B is a continuous monotone operator with B– = ∅, Jλ is a weak relatively nonexpansive mapping.
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