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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.11 No.3

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

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / 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
Lee, Bok-Doo
Lee,, B. , & Lee,, B. (2004). Weakly Relaxed $\alpha$-semi-pseudomonotone Set-valued Variational-like Inequalities. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 11(3), 231-242.

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

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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