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Semicontinuity of bifunctions and applications to regularization methods for equilibrium problems

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Abstract

In this paper, we introduce a concept of semicontinuity on a subset with respect to the whole space and obtain that upper and lower semicontinuity are not needed in the whole space when solving equilibrium problems. The well-known Ky Fan’s minimax inequality theorem is extended and applications to regularization methods for pseudomonotone bilevel equilibrium problems are given.

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Acknowledgments

The author thanks the anonymous referees for their careful reading of this paper and for their valuable comments and suggestions.

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  1. Laboratoire de Mécanique, Physique et Modélisation Mathématique, Université de Médéa, 26000, Médéa, Algeria

    Boualem Alleche

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  1. Boualem Alleche
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Correspondence to Boualem Alleche.

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Alleche, B. Semicontinuity of bifunctions and applications to regularization methods for equilibrium problems. Afr. Mat. 26, 1637–1649 (2015). https://doi.org/10.1007/s13370-014-0308-1

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