Coincidence theorem and existence theorems of solutions for a system of Ky Fan type minimax inequalities in FC-spaces

Ronghua He

Abstract


Let $I$ be any index set. By using some existence theorems of maximal elements for a family of set-valued mappings involving a better admissible set-valued mapping under noncompact setting of $FC$-spaces, we first present some nonempty intersection theorems for a family $\{G_{i}\}_{i\in I}$ in a product space of $FC$-spaces. Next we give a coincidence theorem and a Fan-Browder type fixed point theorem. Finally, as applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems are proved in product $FC$-space, some existence theorems of solutions for a system of Ky Fan type minimax inequalities involving a family of $G_{\cal B}$-majorized mappings defined on the product space of $FC$-space are also obtained. Our results improve and generalize some recent results.

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How to Cite this Article:

Ronghua He, Coincidence theorem and existence theorems of solutions for a system of Ky Fan type minimax inequalities in FC-spaces, Advances in Fixed Point Theory, Vol 2, No 1 (2012), 47-57

Copyright © 2012 Ronghua He. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Advances in Fixed Point Theory

ISSN: 1927-6303

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