A Hybrid Proximal Point Three-Step Algorithm for Nonlinear Set-Valued Quasi-Variational Inclusions System Involving (A,)-Accretive Mappings
نویسندگان
چکیده
The main purpose of this paper is to introduce and study a new class of generalized nonlinear setvalued quasi-variational inclusions system involving A, η -accretive mappings in Banach spaces. By using the resolvent operator due to Lan-Cho-Verma associated with A, η -accretive mappings and the matrix analysis method, we prove the convergence of a new hybrid proximal point three-step iterative algorithm for this system of set-valued variational inclusions and an existence theorem of solutions for this kind of the variational inclusions system. The results presented in this paper generalize, improve, and unify some recent results in this field.
منابع مشابه
Research Article Perturbed Iterative Algorithms for Generalized Nonlinear Set-Valued Quasivariational Inclusions Involving Generalized m-Accretive Mappings
A new class of generalized nonlinear set-valued quasivariational inclusions involving generalizedm-accretive mappings in Banach spaces are studied, which included many variational inclusions studied by others in recent years. By using the properties of the resolvent operator associated with generalized m-accretive mappings, we established the equivalence between the generalized nonlinear set-va...
متن کاملSensitivity Analysis for System of Parametric Generalized Quasi-variational Inclusions Involving R-accretive Mappings
In this paper, using proximal-point mappings technique of Raccretive mappings and the property of the fixed point set of set-valued contractive mappings, we study the behavior and sensitivity analysis of the solution set of the system of parametric generalized quasi-variational inclusions involving R-accretive mappings in real uniformly smooth Banach space. Further under suitable conditions, we...
متن کاملAn Ishikawa-Hybrid Proximal Point Algorithm for Nonlinear Set-Valued Inclusions Problem Based on (A,)-Accretive Framework
A general nonlinear framework for an Ishikawa-hybrid proximal point algorithm using the notion of A, η -accretive is developed. Convergence analysis for the algorithm of solving a nonlinear set-valued inclusions problem and existence analysis of solution for the nonlinear set-valued inclusions problem are explored along with some results on the resolvent operator corresponding to A, η -accretiv...
متن کاملA New System of Nonlinear Fuzzy Variational Inclusions Involving (A,)-Accretive Mappings in Uniformly Smooth Banach Spaces
A new system of nonlinear fuzzy variational inclusions involving A, η -accretive mappings in uniformly smooth Banach spaces is introduced and studiedmany fuzzy variational and variational inequality inclusion problems as special cases of this system. By using the resolvent operator technique associated with A, η -accretive operator due to Lan et al. and Nadler’s fixed points theorem for set-val...
متن کاملIshikawa type iterative algorithm for completely generalized nonlinear quasi-variational-like inclusions in Banach spaces
In this paper, we consider completely generalized nonlinear quasi-variational-like inclusions in Banach spaces and propose an Ishikawa type iterative algorithm for computing their approximate solutions by applying the new notion of Jη-proximal mapping given in [R. Ahmad, A.H. Siddiqi, Z. Khan, Proximal point algorithm for generalized multi-valued nonlinear quasi-variational-like inclusions in B...
متن کامل