Abstract
We introduce and study variational-like inequalities for generalized pseudomonotone set-valued mappings in Banach spaces. By using KKM technique, we obtain the existence of solutions for variational-like inequalities for generalized pseudomonotone set-valued mappings in reflexive Banach spaces. The results presented in this paper are generalizations and improvements of the several well-known results in the literature.
Highlights
Introduction and PreliminariesVariational inequality theory plays an important role in many fields, such as optimal control, mechanics, economics, transportation equilibrium, and engineering science
Inspired and motivated by the results of Fang and Huang [4] and Kutbi and Sintunavarat [15], in this paper, we introduce the concept of weakly relaxed η-α pseudomonotone mapping and by using Knaster Kuratowski Mazurkiewicz (KKM) technique [16], we study some existence of solution for variational-like inequality for set-valued pseudomonotone mapping
Remark 2. (i) If φ(x, x) = 0 in Definition 1 we have the following pseudomonotone concept defined in Kang et al [13]:
Summary
College of Engineering, Qassim University, P.O. Box 6677, Buraidah, Al-Qassim 51452, Saudi Arabia. We introduce and study variational-like inequalities for generalized pseudomonotone set-valued mappings in Banach spaces. By using KKM technique, we obtain the existence of solutions for variational-like inequalities for generalized pseudomonotone setvalued mappings in reflexive Banach spaces. The results presented in this paper are generalizations and improvements of the several well-known results in the literature
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