Abstract
A new system of nonlinear fuzzy variational inclusions involving -accretive mappings in uniformly smooth Banach spaces is introduced and studied many fuzzy variational and variational inequality (inclusion) problems as special cases of this system. By using the resolvent operator technique associated with -accretive operator due to Lan et al. and Nadler's fixed points theorem for set-valued mappings, an existence theorem of solutions for this system of fuzzy variational inclusions is proved. We also construct some new iterative algorithms for the solutions of this system of nonlinear fuzzy variational inclusions in uniformly smooth Banach spaces and discuss the convergence of the sequences generated by the algorithms in uniformly smooth Banach spaces. Our results extend, improve, and unify many known results in the recent literatures.
Highlights
Variational inequality was initially studied by Stampacchia 1 in 1964
The method based on the resolvent operator technique is a generalization of the projection method and has been widely used to solve variational inclusions
Lan and Verma 54, by using the concept of A, η -accretive mappings, the resolvent operator technique associated with A, η -accretive mappings, introduced and studied a new class of nonlinear fuzzy variational inclusion systems with A, η -accretive mappings in Banach spaces and construct some new iterative algorithms to approximate the solutions of the nonlinear fuzzy variational inclusion systems
Summary
Variational inequality was initially studied by Stampacchia 1 in 1964. In order to study many kinds of problems arising in industrial, physical, regional, economical, social, pure, and applied sciences, the classical variational inequality problems have been extended and generalized in many directions. Lan and Verma 54 , by using the concept of A, η -accretive mappings, the resolvent operator technique associated with A, η -accretive mappings, introduced and studied a new class of nonlinear fuzzy variational inclusion systems with A, η -accretive mappings in Banach spaces and construct some new iterative algorithms to approximate the solutions of the nonlinear fuzzy variational inclusion systems. By using the resolvent operator associated with A, η -mappings due to Lan et al and Nadler’s fixed points theorem, we construct some new iterative algorithms for approximating the solutions of this system of nonlinear fuzzy variational inclusions in Banach spaces and prove the existence of solutions and the convergence of the sequences generated by the algorithms in q-uniformly smooth Banach spaces. The results presented in this paper improve and extend the corresponding results of 29–35, 38, 39, 55–60 and many other recent works
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