Abstract
In this paper, we introduce a new iterative algorithm by the relaxed extragradient-like method for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of solutions of a more general system of variational inequalities for finite inverse strongly monotone mappings and the set of solutions of a fixed point problem of a strictly pseudocontractive mapping in a Hilbert space. Then we prove strong convergence of the scheme to a common element of the three above described sets.
Highlights
1 Introduction In this paper, we assume that H is a real Hilbert space with the inner product ·, · and the induced norm · and C is a nonempty closed convex subset of H
In this paper, motivated and inspired by the above facts, we study a new iterative algorithm by the relaxed extragradient-like method for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of solutions of a more general system of variational inequalities for finite inverse strongly monotone mappings and the set of solutions of a fixed point problem of a strictly pseudocontractive mapping in a Hilbert space
All authors read and approved the final manuscript
Summary
We assume that H is a real Hilbert space with the inner product ·, · and the induced norm · and C is a nonempty closed convex subset of H. In this paper, motivated and inspired by the above facts, we study a new iterative algorithm by the relaxed extragradient-like method for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of solutions of a more general system of variational inequalities for finite inverse strongly monotone mappings and the set of solutions of a fixed point problem of a strictly pseudocontractive mapping in a Hilbert space. Assume that F : C × C → R satisfies (A )-(A ), B : C → H is a continuous monotone mapping and let φ : C → R be a lower semicontinuous and convex function. {Fk}Mk= be a family of bifunctions from C × C into R satisfying (A )-(A ), let {φk}Mk= : C → R be a family of lower semicontinuous and convex functions and let {Bk}Mk= be a family of βkinverse-strongly monotone mappings from C into H.
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