Nonlinear relaxed cocoercive variational inclusions involving (A, η)-accretive mappings in banach spaces

Authors:
Heng-You Lan;Yeol Je Cho;R. U. Verma
Affiliations:
-;-;-
Venue:
Computers & Mathematics with Applications
Year:
2006

Citing 2
Cited 11

Inequalities in Banach spaces with applications

Nonlinear Analysis: Theory, Methods & Applications
Existence and algorithm of solutions for generalized mixed implicit quasi-variational inequalities

Applied Mathematics and Computation

Iterative algorithms for a new system of nonlinear variational inclusions with (A,η)-accretive mappings in Banach spaces

Computers & Mathematics with Applications
The existence and uniqueness of solution and the convergence of a multi-step iterative algorithm for a system of variational inclusions with (A, η, m)-accretive operators

Journal of Global Optimization
Generalized nonlinear random (A,η)-accretive equations with random relaxed cocoercive mappings in Banach spaces

Computers & Mathematics with Applications
The p-step iterative algorithm for a system of generalized mixed quasi-variational inclusions with (A,η)-accretive operators in q-uniformly smooth banach spaces

Journal of Computational and Applied Mathematics
Convergence and stability of iterative algorithm for a new system of (A,η)-accretive mapping inclusions in Banach spaces

Computers & Mathematics with Applications
A novel proof of the existence of solutions for a new system of generalized mixed quasi-variational-like inclusions involving (A, η, m)-accretive operators

Journal of Global Optimization
A new system of generalized nonlinear quasi-variational-like inclusions with A-monotone operators in Banach spaces

Journal of Computational and Applied Mathematics
(H(·,·),η)-accretive operators with an application for solving set-valued variational inclusions in Banach spaces

Computers & Mathematics with Applications
On a new system of generalized mixed quasi-variational-like inclusions involving (A,η,m)-accretive operators with applications

Journal of Computational and Applied Mathematics
New perturbed finite step iterative algorithms for a system of extended generalized nonlinear mixed quasi-variational inclusions

Computers & Mathematics with Applications
The generalized relaxed proximal point algorithm involving A-maximal-relaxed accretive mappings with applications to Banach spaces

Mathematical and Computer Modelling: An International Journal

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Abstract

In this paper, we introduce a new concept of (A, @h)-accretive mappings, which generalizes the existing monotone or accretive operators. We study some properties of (A, @h)-accretive mappings and define resolvent operators associated with (A, @h)-accretive mappings. By using the new resolvent operator technique, we also construct a new perturbed iterative algorithm with mixed errors for a class of nonlinear relaxed Cocoercive variational inclusions involving (A, @h)-accretive mappings and study applications of (A, @h)-accretive mappings to the approximation-solvability of this class of nonlinear relaxed Cocoercive variational inclusions in q-uniformly smooth Banach spaces. Our results improve and generalize the corresponding results of recent works.