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Existence results for vector equilibrium problems given by a sum of two functions

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Abstract

We obtain existence results for the weak vector equilibrium problem where the function involved is a sum of two functions, and the assumptions are required separately on each of these functions. We show that some earlier results of this type contain too demanding assumptions. We relax several of these assumption without loosing the results. The special case of reflexive Banach spaces is also studied, where we make use of the fact that closed balls are weakly compact.

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Acknowledgments

This work was supported by a grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, project number PN-II-ID-PCE-2011-3-0024. The authors wish to thank the two anonymous referees for their helpful comments, which helped them to improve the presentation of the paper.

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  1. Faculty of Mathematics and Computer Science, Babes-Bolyai University, 1 M. Kogalniceanu, 400084, Cluj-Napoca, Romania

    Gábor Kassay & Mihaela Miholca

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  1. Gábor Kassay
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  2. Mihaela Miholca
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Correspondence to Gábor Kassay.

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Kassay, G., Miholca, M. Existence results for vector equilibrium problems given by a sum of two functions. J Glob Optim 63, 195–211 (2015). https://doi.org/10.1007/s10898-014-0264-1

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