ON GENERALIZED NONLINEAR QUASI-VARIATIONAL-LIKE INCLUSIONS DEALING WITH (h, η)-PROXIMAL MAPPING
نویسندگان
چکیده
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 nonlinear quasi-variational-like inclusion is suggested. The existence and uniqueness theorems of solution for the generalized nonlinear quasi-variational-like inclusion are established. The convergence and stability results of iterative sequence generated by the perturbed three-step iterative algorithm with errors are discussed.
منابع مشابه
Generalized Multivalued Nonlinear Quasi - Variational like Inclusions
In this paper, we suggest and analyze a class of iterative schemes for solving generalized multivalued nonlinear quasi-variational like inclusion problems using the concept of η-subdifferential and η-proximal mappings of a proper functional on Hilbert spaces. A detailed convergence analysis of our method is also included.
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 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 کاملA new system of generalized quasi-variational-like inclusions with noncompact valued mappings
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 algori...
متن کامل