Abstract
In this article, we introduce and consider the three-step iterative algorithms for solving a new system of generalized mixed variational inequalities involving different three multi-valued operators. In this study, we use a generalized f-projection method for finding the solutions of generalized system of mixed variational inequalities in Banach spaces. Our result in this article improves and generalizes some known corresponding results in the literature.2000 Mathematics Subject Classification: 47H10; 47H19; 49J40.
Highlights
Let B be a real Banach space which dual space B* and C be a nonempty closed convex subset of B
Let 〈·, ·〉 be the dual pair between B and B*, J denotes the normalized duality mapping and R be the field of real numbers
In 2007, Wu and Huang [13], they proved some properties of the generalized f-projection operator and proposed iterative method of approximating solutions for a class of generalized variational inequalities in Banach spaces
Summary
Let B be a real Banach space which dual space B* and C be a nonempty closed convex subset of B. In 2007, Wu and Huang [13], they proved some properties of the generalized f-projection operator and proposed iterative method of approximating solutions for a class of generalized variational inequalities in Banach spaces. In 2009, Fan et al [2] presented some basic results for the generalized f-projection operator and discussed the existence of solutions and approximation of the solutions for generalized variational inequalities in noncompact subsets of Banach spaces. Using the generalized f-projection operator technique, they introduced two-step iterative methods for solving the system of mixed variational inequalities and proved the convergence of the proposed iterative methods under suitable conditions in Banach spaces. Motivated and inspired by the recent research studies in this fascinating area, the purpose of this article is to introduce and analyze three-step iterative algorithm for finding a new system of generalized mixed variational inequality problems with three difference multi-valued operators in Banach spaces.
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