Abstract
We introduce and study a new general system of nonlinear variational inclusions involving generalizedm-accretive mappings in Banach space. By using the resolvent operator technique associated with generalizedm-accretive mappings due to Huang and Fang, we prove the existence theorem of the solution for this variational inclusion system in uniformly smooth Banach space, and discuss convergence and stability of a class of new perturbed iterative algorithms for solving the inclusion system in Banach spaces. Our results presented in this paper may be viewed as an refinement and improvement of the previously known results.
Highlights
Let m a real be a given positive Banach space with integer, for any dual space Xi∗. i∈ Xi, {1, Xi∗. . , m}, Xi endowed with the norm ‖ ⋅ ‖, and ⟨⋅, ⋅⟩ the dual pair between Xi andXi∗
We introduce and study a new general system of nonlinear variational inclusions involving generalized m-accretive mappings in Banach space
By using the resolvent operator technique associated with generalized m-accretive mappings due to Huang and Fang, we prove the existence theorem of the solution for this variational inclusion system in uniformly smooth Banach space, and discuss convergence and stability of a class of new perturbed iterative algorithms for solving the inclusion system in Banach spaces
Summary
Let m a real be a given positive Banach space with integer, for any dual space Xi∗. , m}, Xi endowed with the norm ‖ ⋅ ‖, and ⟨⋅, ⋅⟩ the dual pair between Xi and. We consider the following new general system for nonlinear variational inclusion involving generalized m-accretive mappings. Some special cases of the problem (1) had been studied by many authors. M), the Hilbert spaces, was introduced and studied as general system of monotone nonlinear variational inclusions problems by. Problem (7) is called a system of strongly nonlinear quasivariational inclusion involving generalized m-accretive mappings, it is considered and studied by Lan [19]. Many authors discussed stability of the iterative sequence generated by the algorithm for solving the problems that they studied. Motivated and inspired by the above works, the main purpose of this paper is to introduce and study the new general system of nonlinear variational inclusions (1) involving generalized m-accretive mapping in uniformly smooth Banach spaces. By using the resolvent operator technique for generalized m-accretive, we prove the existence theorem of the solution for this kind of system of variational inclusions in Banach spaces and discuss the convergence and stability of a new perturbed iterative algorithm for solving this general system of nonlinear variational inclusions in Banach spaces
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