A viscosity iterative algorithm for the optimization problem system

Abstract

In this paper, we suggest and analysis a viscosity iterative algorithm for finding a common element of the set of solution of a mixed equilibrium problem and the set the of solutions of a variational inequality and all common fixed points of a nonexpansive semigroup. This algorithm strongly converges to an element which solves an optimization problem system. Finally, some examples and numerical results are also given.

A hybrid projective method for solving system of equilibrium problems with demicontractive mappings applicable in image restoration problems

“…Inspired and motivated by above works and the work of other studies 10,11,17,19,[29][30][31] in this paper, we modify CQ methods for finding a common solution set of system found in equilibrium problem and the fixed-point set of a finite family of demicontractive mappings. Further, we prove a strong convergence theorem for the sequences generated by iterative method and derive some consequences which are new and interesting.…”

Viscosity approximation method for modified split generalized equilibrium and fixed point problems

“…The viscosity iterative algorithm is one of the algorithms that have been used extensively by authors to approximate solutions of fixed point problems and optimization problems. The algorithm is constructed in such a way that it also solves some variational inequality problem (see [6,21,28] and the references therein). In 2017, Deepho et al [16] considered the viscosity iterative algorithm to approximate a common element of the set of solutions of a split variational inclusion problem of a finite family of k-strictly pseudo-contractive nonself mappings.…”