Variational-Like Inequalities with Generalized Monotone Mappings in Banach Spaces

Y.P. Fang and N.J. Huang
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Y.P. Fang: Sichuan University
N.J. Huang: Sichuan University

Journal of Optimization Theory and Applications, 2003, vol. 118, issue 2, No 6, 327-338

Abstract: Abstract In this paper, we introduce two classes of variational-like inequalities with generalized monotone mappings in Banach spaces. Using the KKM technique, we obtain the existence of solutions for variational-like inequalities with relaxed η–α monotone mappings in reflexive Banach spaces. We present also the solvability of variational-like inequalities with relaxed η–α semimonotone mappings in arbitrary Banach spaces by means of the Kakutani-Fan-Glicksberg fixed-point theorem. The results presented in this paper extend and improve the corresponding results of Refs. 1–6.

Keywords: Variational-like inequalities; generalized monotone mappings; KKM mappings; η-hemicontinuity; η-coercivity (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (11)

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DOI: 10.1023/A:1025499305742

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