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New Generalized R-KKM Type Theorems in General Topological Spaces and Applications

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Abstract

In this paper, some new generalized R-KKM type theorems for generalized R-KKM mappings with finitely closed values and with finitely open values are established in noncompact topological spaces without any convexity structure under much weaker assumptions. As applications, some new minimax inequalities, saddle point theorem and equilibrium existence theorem for equilibrium problems with lower and upper bounds are established in general noncompact topological spaces. These theorems unify and generalize many known results in the literature.

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Authors and Affiliations

  1. College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, P. R. China

    Xie Ping Ding

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  1. Xie Ping Ding
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Correspondence to Xie Ping Ding.

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This project is supported by Natural Science Foundation of Sichuan Education Department of China (2003A081) and SZD0406

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Ding, X.P. New Generalized R-KKM Type Theorems in General Topological Spaces and Applications. Acta Math Sinica 23, 1869–1880 (2007). https://doi.org/10.1007/s10114-005-0876-y

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  • DOI: https://doi.org/10.1007/s10114-005-0876-y

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