Existence of Solutions of New Generalized Mixed Vector Variational-Like Inequalities in Reflexive Banach Spaces

Somyot Plubtieng () and Tipphawan Thammathiwat ()
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Somyot Plubtieng: Naresuan University
Tipphawan Thammathiwat: Naresuan University

Journal of Optimization Theory and Applications, 2014, vol. 162, issue 2, No 14, 589-604

Abstract: Abstract In this paper, we extend the concept of monotonicity for a vector set-valued mapping to semimonotonicity for a vector set-valued mapping. Then, we prove solvability results for a class of new generalized mixed vector variational-like inequalities by applying the Fan-KKM theorem and Nadler’s result. On the other hand, we introduce the concepts of complete semicontinuity and strong semicontinuity for vector multivalued mappings. Moreover, by using the Brouwer fixed point theorem, we prove the solvability for the class of generalized vector variational-like inequalities without monotonicity assumption. Using this result, we obtain a theorem and corollary that improve and extend some known results.

Keywords: Generalized mixed vector variational-like inequalities; Semimonotonicity; Complete semicontinuous; Fan-KKM theorem; Brouwer fixed point theorem (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10957-013-0322-8

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