Equivalent forms of a generalized KKM theorem and their applications |
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| Authors: | Mircea Balaj |
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| Affiliation: | a Department of Mathematics, University of Oradea, Oradea 411087, Oradea, Romania
b Department of Mathematics, National Changhua University of Education, Changhua, 50058, Taiwan |
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| Abstract: | In this paper, we study various types of variational relation problems. We establish the existence of solutions for these types of problems and point out some important particular cases and their applications. We also show that some existence theorems of solution for these types of problems and some existence theorems of variational inclusion problems are equivalent to a generalized KKM theorem. Applying our results we obtain existence theorems of common fixed point, generalized maximal element theorems, a generalized coincidence theorems and a section theorem. |
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| Keywords: | Variational relation problem Better admissible class KKM theorem Coincidence theorem Variational inclusion problem Maximal element theorem Common fixed point theorem |
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