A viscosity of Cesaro mean approximation method for split generalized equilibrium, variational inequality and fixed point problems

Abstract

In this paper, we introduce and study an iterative viscosity approximation method by modified Cesàro mean approximation for finding a common solution of split generalized equilibrium, variational inequality and fixed point problems. Under suitable conditions, we prove a strong convergence theorem for the sequences generated by the proposed iterative scheme. The results presented in this paper generalize, extend and improve the corresponding results of Shimizu

On solving the split generalized equilibrium problem and the fixed point problem for a countable family of nonexpansive multivalued mappings

“…The authors also gave an iterative algorithm to find a common element of the solution sets of the split generalized equilibrium problem in real Hilbert spaces; for more details, we refer to [7][8][9]. If ϕ 1 = 0 and ϕ 2 = 0, then the split generalized equilibrium problem reduces to the split equilibrium problem; see [10].…”

An inertial based forward–backward algorithm for monotone inclusion problems and split mixed equilibrium problems in Hilbert spaces

“…for all y ∈ C. Since v n q, therefore utilizing (25) and (C4), the above estimate implies that F(y,q) + φ f (q)φ f (y) ≤ 0 for all y ∈ C.…”

“…This formalism is also at the core of modeling of many inverse problems arising for phase retrieval and other real-world problems; for instance, in sensor networks in computerized tomography and data compression; see, for example, [18,21]. Some methods have been proposed and analyzed to solve split equilib-rium problem and mixed split equilibrium problem in Hilbert spaces; see, for example, [24,25,28,29,36,37,51,54,59,60] and the references cited therein. Inspired and motivated by the above-mentioned results and the ongoing research in this direction, we aim to employ the modified inertial forward-backward algorithm to find a common solution of the monotone inclusion problem and the SEP in Hilbert spaces.…”

Strong Convergence of New Two-Step Viscosity Iterative Approximation Methods for Set-Valued Nonexpansive Mappings in CAT(0) Spaces

“…For more works on the convergence analysis of (viscosity) iteration approximation method for (split) fixed point problems, one can refer to [20][21][22][23][24][25][26][27].…”