A new system of generalized quasi-variational-like inclusions with noncompact valued mappings
نویسنده
چکیده
Correspondence: chwhappy@163. com Department of Science, Nanchang Institute of Technology, Nanchang 330099, P. R. China Abstract In this article, we introduce and study a new system of generalized quasi-variationallike inclusions with noncompact valued mappings. By using the h-proximal mapping technique, we prove the existence of solutions and the convergence of some new N-step iterative algorithms for this system of generalized quasi-variational-like inclusions. Our results extend and improve some known results in the literature. Mathematics Subject Classification 2000: 49H09; 49J40; 49H10.
منابع مشابه
Ishikawa 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 کاملA SYSTEM OF GENERALIZED VARIATIONAL INCLUSIONS INVOLVING G-eta-MONOTONE MAPPINGS
We introduce a new concept of general $G$-$eta$-monotone operator generalizing the general $(H,eta)$-monotone operator cite{arvar2, arvar1}, general $H-$ monotone operator cite{xiahuang} in Banach spaces, and also generalizing $G$-$eta$-monotone operator cite{zhang}, $(A, eta)$-monotone operator cite{verma2}, $A$-monotone operator cite{verma0}, $(H, eta)$-monotone operator cite{fanghuang}...
متن کاملA Hybrid Proximal Point Three-Step Algorithm for Nonlinear Set-Valued Quasi-Variational Inclusions System Involving (A,)-Accretive Mappings
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 a...
متن کاملResearch 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 کاملON GENERALIZED NONLINEAR QUASI-VARIATIONAL-LIKE INCLUSIONS DEALING WITH (h, η)-PROXIMAL MAPPING
In this paper, a new class of (h, η)-proximal mappings for proper functionals in Hilbert spaces is introduced. The existence and Lipschitz continuity of the (h, η)-proximal mappings for proper functionals are proved. A class of generalized nonlinear quasi-variational-like inclusions in Hilbert spaces is introduced. A perturbed three-step iterative algorithm with errors for the generalized nonli...
متن کامل