The main purpose of this paper is to find a common element in the solution set of equilibrium problem and fixed point problem of non-expansive mappings in the real Hilbert space with the help of normal S-iteration process. Also, under some acceptable assumptions, we prove the sequences induced by above stated process converge weakly to a point in the solution set of above stated problems. At the end, we give a numerical example to justify our work. The results studied in this work philosophize and boost some contemporary and known results in this direction.
The purpose of this paper is to recommend an iterative scheme to approximate a common element of the solution sets of the split problem of variational inclusions, split generalized equilibrium problem and fixed point problem for non-expansive mappings. We prove that the sequences generated by the recommended iterative scheme strongly converge to a common element of solution sets of stated split problems. In the end, we provide a numerical example to support and justify our main result. The result studied in this paper generalizes and extends some widely recognized results in this direction.
In this article, we suggest and study a new inertial algorithm combining inertial extrapolation, S‐iteration process and viscosity approximation method for computing a common solution of an equilibrium problem and a family of nonexpansive operators in real Hilbert space. We provide a strong convergence result of the suggested algorithm under some simple assumptions on control sequences. Further, we compare our suggested algorithm with some existing well‐known algorithms by an analytical example. Some prominent recent findings in this field have been improved, generalized, and extended as an outcome of this paper.
In this study, we propose an inertial extragradient algorithm for solving a split generalized equilibrium problem as well as a split feasibility and common fixed point problem. We demonstrate that, under certain reasonable assumptions, the sequences induced by the proposed algorithm converge strongly to a solution of the corresponding problem. In addition, with the help of a numerical example, we demonstrate the efficiency of proposed algorithm. As a result of this paper, some recent well-known results in this area have been improved, generalized, and extended.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.