A hybrid viscosity iterative method with averaged mappings for split equilibrium problems and fixed point problems

Abstract

In this paper, with the help of averaged mappings, we introduce and study a hybrid iterative method to approximate a common solution of a split equilibrium problem and a fixed point problem of a finite collection of nonexpansive mappings. We prove that the sequences generated by the iterative scheme strongly converges to a common solution of the above-said problems. We give some numerical examples to ensure that our iterative scheme is more efficient than the methods of Plubtieng and Punpaeng (

Parallel hybrid viscosity method for fixed point problems, variational inequality problems and split generalized equilibrium problems

“…And then we establish the corresponding strong convergence theorem under suitable conditions. We study more general split equilibrium problems and fixed point problems of operators than those in [18]. Our results in this paper improve and extend many recent results in the literature.…”

“…In 2017, Majee and Nahak [18] introduced a hybrid viscosity iterative method to approximate a common solution of a split equilibrium problem and a fixed point problem of a finite collection of nonexpansive mappings; Onjai-uea and Phuengrattana [19] studied iterative algorithms for solving split mixed equilibrium problems and fixed point problems of hybrid multivalued mappings in real Hilbert spaces; Sitthithakerngkiet et al [20] proposed an iterative method for finding a common solution of a single split generalized equilibrium problem, variational inequality problem and fixed point problem of nonexpansive mapping in Hilbert spaces. For recent developments in the analysis technique and algorithm design, see [21][22][23][24][25] and the references therein.…”

Hybrid iterative methods for multiple sets split feasibility problems

“…Lemma 2.7. ( [28]) Let H be a Hilbert space. Let f : H → H be a ρ-Lipschitzian mapping and let A : H → H be a strongly positive bounded linear operator with coefficient δ > 0.…”

Graph convergence with an application for system of variational inclusions and fixed-point problems

“…The existence of a strong connection between the variational inequality problems and the fixed-point problems motivated many investigators to study the problem of finding common elements of the set of solutions of variational inequalities/inclusions and the set of fixed points of given operators. For more details and information, the reader is referred to [4,[38][39][40][41][42][43][44][45][46] and the references therein.…”