Abstract
Let X be a Banach space with both q-uniformly smooth and uniformly convex structures. This article introduces and considers a general extragradient implicit method for solving a general system of variational inequalities (GSVI) with the constraints of a common fixed point problem (CFPP) of a countable family of nonlinear mappings { S n } n = 0 ∞ and a monotone variational inclusion, zero-point, problem. Here, the constraints are symmetrical and the general extragradient implicit method is based on Korpelevich’s extragradient method, implicit viscosity approximation method, Mann’s iteration method, and the W-mappings constructed by { S n } n = 0 ∞ .
Highlights
Let X be Banach space and J be duality set-valued mapping on X
The symmetry system is quite applicable in lots of convex optimizations and finds a lot of applications in applied sciences, such as intensity modulated radiation therapy, signal processing, image reconstruction, and so on. The model of these problems can be rewritten as a variational inequality, which is a special case of the system that is, the unconstrained minimization problem min f( x ) := f ( x ) + IC ( x ), x∈ H
Motivated by the above research results, the purpose of this research is to obtain, on the Banach space with uniform convexness and q-uniform smoothness, for example, L p with p > 1, a feasibility point in the solution set of the Equation (1) involving a common fixed point problem (CFPP) of nonlinear operator {Sn }∞
Summary
Let X be Banach space and J be duality set-valued mapping on X. With two real constants μ1 and μ2 > 0 This is called a symmetrical variational system. This system was first introduced and studied in [1]. The model of these problems can be rewritten as a variational inequality, which is a special case of the system that is, the unconstrained minimization problem min f( x ) := f ( x ) + IC ( x ), x∈ H where f : H → R is a real-valued convex function that is assumed to be continuously differentiable and IC ( x ) is the indicator of C: 0, x ∈ C, IC ( x ) =
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