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Intersection theorems for generalized weak KKM set‐valued mappings with applications in optimization

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  • Mircea Balaj

Abstract

In this paper, we introduce the concept of generalized weak KKM mapping that is more general than many others encountered in the KKM theory. Then, two previous intersection theorems of the author are extended from weak KKM mappings to generalized weak KKM mappings. Applications of these results to set‐valued equilibrium problems and minimax inequalities are given in the last two sections.

Suggested Citation

  • Mircea Balaj, 2021. "Intersection theorems for generalized weak KKM set‐valued mappings with applications in optimization," Mathematische Nachrichten, Wiley Blackwell, vol. 294(7), pages 1262-1276, July.
    • Handle: RePEc:bla:mathna:v:294:y:2021:i:7:p:1262-1276
    DOI: 10.1002/mana.201900243
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    References listed on IDEAS

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    4. Ravi P. Agarwal & Mircea Balaj & Donal O’Regan, 2017. "Common Fixed Point Theorems in Topological Vector Spaces via Intersection Theorems," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 443-458, May.
    5. Werner Oettli & Dirk Schläger, 1998. "Existence of equilibria for monotone multivalued mappings," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(2), pages 219-228, November.
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    7. Ravi P. Agarwal & Mircea Balaj & Donal O’Regan, 2018. "Intersection Theorems with Applications in Optimization," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 761-777, December.
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