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Strong convergence theorems for relatively quasi-nonexpansive mappings, variational inequality problems and systems of generalized mixed equilibrium problems

100%

Shehu Y. , Oguguo O.

Journal of Applied Analysis

2012

tom Vol. 18, nr 1

69-95

In this paper, we construct a new iterative scheme by hybrid methods to approximate a common element in the fixed points set of an infinite family of relatively quasi-nonexpansive mappings, the solutions set of a variational inequality problem and the solutions set of a system of generalized mixed equilibrium problems in a 2-uniformly convex real Banach space which is also uniformly smooth. Then, we prove strong convergence of the scheme to a common element of the three sets. We give several applications of our results in a Banach space. Our results extend many known recent results in the literature.

An iterative approximation of common solutions of split generalized vector mixed equilibrium problem and some certain optimization problems

100%

Mewomo O. T. , Oyewole O. K.

Demonstratio Mathematica

2021

tom Vol. 54, nr 1

335--358

In this paper, we study the problem of finding a common solution of split generalized vector mixed equlibrium problem (SGVMEP), fixed point problem (FPP) and variational inequality problem (VIP). We propose an inertial-type iterative algorithm, which uses a projection onto a feasible set and a linesearch, which can be easily calculated. We prove a strong convergence of the sequence generated by the proposed algorithm to a common solution of SGVMEP, fixed point of a quasi- ϕ -nonexpansive mapping and VIP for a general class of monotone mapping in 2-uniformly convex and uniformly smooth Banach space E1 and a smooth, strictly convex and reflexive Banach space E2 . Some numerical examples are presented to illustrate the performance of our method. Our result improves some existing results in the literature.