System of nonlinear variational inclusion problems with (A, η)-maximal monotonicity in Banach spaces
نویسندگان
چکیده
This paper deals with a new system of nonlinear variational inclusion problems involving (A, η)-maximal relaxed monotone and relative (A, η)-maximal monotone mappings in 2-uniformly smooth Banach spaces. Using the generalized resolvent operator technique, the approximation solvability of the proposed problem is investigated. An iterative algorithm is constructed to approximate the solution of the problem. Convergence analysis of the proposed algorithm is investigated. Similar results are also proved for other system of variational inclusion problems involving relative (A, η)maximal monotone mappings and (H, η)-maximal monotone mappings.
منابع مشابه
Implicit Variational Inclusions and Algorithms Involving (A, η)-monotone Operators in 2-uniformly Smooth Banach Spaces
This paper deals with a new class of nonlinear set valued implicit variational inclusion problems involving (A, η)-monotone mappings in 2-uniformly smooth Banach spaces. Semi-inner product structure has been used to study the (A, η)-monotonicity. Using the generalized resolvent operator technique and the semi-inner product structure, the approximation solvability of the proposed problem is inve...
متن کاملGeneral Framework for Proximal Point Algorithms on (a, Η)-maximal Monotonicity for Nonlinear Variational Inclusions
General framework for proximal point algorithms based on the notion of (A, η)-maximal monotonicity (also referred to as (A, η)monotonicity in literature) is developed. Linear convergence analysis for this class of algorithms to the context of solving a general class of nonlinear variational inclusion problems is successfully achieved along with some results on the generalized resolvent correspo...
متن کاملON MULTIVALUED NONLINEAR VARIATIONAL INCLUSION PROBLEMS WITH (A, eta)-ACCRETIVE MAPPINGS IN BANACH SPACES
Based on the notion of (A,η)-accretive mappings and the resolvent operators associated with (A,η)-accretive mappings due to Lan et al., we study a new class of multivalued nonlinear variational inclusion problemswith (A,η)-accretivemappings in Banach spaces and construct some new iterative algorithms to approximate the solutions of the nonlinear variational inclusion problems involving (A,η)-ac...
متن کاملGeneral Nonlinear Random Set-valued Variational Inclusion Problems with Random Fuzzy Mappings in Banach Spaces
This paper is dedicated to study a new class of general nonlinear random A-maximal m-relaxed η-accretive (so called (A, η)-accretive [49]) equations with random relaxed cocoercive mappings and random fuzzy mappings in q-uniformly smooth Banach spaces. By utilizing the resolvent operator technique for A-maximal m-relaxed η-accretive mappings due to Lan et al. and Chang’s lemma [13], some new ite...
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 کامل