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Variational-Like Inequalities with Generalized Monotone Mappings in Banach Spaces

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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.

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Authors and Affiliations

  1. Department of Mathematics, Sichuan University, Chengdu, Sichuan, P. R. China

    Y.P. Fang (Graduate) & N.J. Huang (Professor, Department of Mathematics, Sichuan University, Chengdu, Sichuan, P. R. China)

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  1. Y.P. Fang
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  2. N.J. Huang
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Fang, Y., Huang, N. Variational-Like Inequalities with Generalized Monotone Mappings in Banach Spaces. Journal of Optimization Theory and Applications 118, 327–338 (2003). https://doi.org/10.1023/A:1025499305742

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