Weakly Relaxed $\alpha$-semi-pseudomonotone Set-valued Variational-like Inequalities

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2004, v.11 no.3, pp.231-242

Lee, Byung-Soo (Department of Matematics, Kyungsung University)
Lee, Bok-Doo (Department of Mathematics, Kyungsung University)

Lee, Byung-Soo, & Lee, Bok-Doo. (2004). WEAKLY RELAXED <TEX>$\alpha$</TEX>-SEMI-PSEUDOMONOTONE SET- VALUED VARIATIONAL-LIKE INEQUALITIES. 한국수학교육학회지시리즈B:순수및응용수학, 11(3), 231-242.

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Abstract

In this paper, we introduce weakly relaxed <TEX>$\alpha$</TEX>-pseudomonotonicity and weakly relaxed <TEX>$\alpha$</TEX>-semi-pseudomonotonicity of set-valued maps. Using the KKM technique, we obtain existence of solutions to the variational-like inequalities with weakly relaxed <TEX>$\alpha$</TEX>-pseudomor.otone set-valued maps in reflexive Banach spaces. We also present the solvability of the variational-like inequalities with weakly relaxed <TEX>$\alpha$</TEX>-semi-pseudomonotone set-valued maps in arbitrary Banach spaces using Kakutani-Fan-Glicksberg fixed point theorem.

keywords: weakly relaxed <tex> $\alpha$</tex>-pseudomonotone, weakly relaxed <tex> ${\alpha}$</tex>-semi-pseudomonotone, KKM map, η-hemicontinuity, F-KKM theorem, η-coercivity, variational-like inequality

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논문 상세

Vol.11 No.3

WEAKLY RELAXED <TEX>$\alpha$</TEX>-SEMI-PSEUDOMONOTONE SET- VALUED VARIATIONAL-LIKE INEQUALITIES

Weakly Relaxed $\alpha$-semi-pseudomonotone Set-valued Variational-like Inequalities

Abstract

한국수학교육학회지시리즈B:순수및응용수학