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Inequality problems of quasi-hemivariational type involving set-valued operators and a nonlinear term

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Abstract

The aim of this paper is to establish the existence of at least one solution for a general inequality of quasi-hemivariational type, whose solution is sought in a subset K of a real Banach space E. First, we prove the existence of solutions in the case of compact convex subsets and the case of bounded closed and convex subsets. Finally, the case when K is the whole space is analyzed and necessary and sufficient conditions for the existence of solutions are stated. Our proofs rely essentially on the Schauder’s fixed point theorem and a version of the KKM principle due to Ky Fan (Math Ann 266:519–537, 1984).

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Authors and Affiliations

  1. Institute of Mathematics “Simion Stoilow” of the Romanian Academy, 014700, Bucharest, Romania

    Nicuşor Costea & Vicenţiu Rădulescu

  2. Department of Mathematics, University of Craiova, 200585, Craiova, Romania

    Vicenţiu Rădulescu

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  1. Nicuşor Costea
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  2. Vicenţiu Rădulescu
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Correspondence to Vicenţiu Rădulescu.

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Costea, N., Rădulescu, V. Inequality problems of quasi-hemivariational type involving set-valued operators and a nonlinear term. J Glob Optim 52, 743–756 (2012). https://doi.org/10.1007/s10898-011-9706-1

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  • DOI: https://doi.org/10.1007/s10898-011-9706-1

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