Equilibrium Problems and Minimax Inequalities for Mappings with Noncompact Domain
- Department of Mathematics, Sheikh Bahai University, Isfahan, IRAN.
In this paper we consider equilibrium problem and introduce minimization problem such as equilibrium problem. We also investigated minimax inequalitiy of Ky Fan and we proved a minimax inequality of mapping with non-compact domain by using the coincidence theorem, then given a minimax inequality for mappings with noncompact domain. As its direct consequences some minimax inequalities and minimax theorems are obtained.
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Mahdiyeh Farshidzad, Equilibrium Problems and Minimax Inequalities for Mappings with Noncompact Domain, Journal of Mathematics and Computer Science, 9 (2014), no. 3, 157 - 164
Farshidzad Mahdiyeh, Equilibrium Problems and Minimax Inequalities for Mappings with Noncompact Domain. J Math Comput SCI-JM. (2014); 9(3):157 - 164
Farshidzad, Mahdiyeh. "Equilibrium Problems and Minimax Inequalities for Mappings with Noncompact Domain." Journal of Mathematics and Computer Science, 9, no. 3 (2014): 157 - 164
- Equilibrium problem
- Minimax theorem
- Ky Fan’s inequality
- Noncompact domain.
F. E. Browder, Coincidence theorems, minimax theorems and variational inequalities, Contemp. Math., Amer Math. Soc., Providence, 26 (1984), 67-80
O. Chadil, Z. chbaniz, H. Riahi, Equilibium problems with Generalized MonotonBifunctions and Applications to Variational Inequalities, Journal of Optimization Theory and Applications, 105 (2000), 299 - 323
C. W. Ha, Minimax and fixed point theorems, Math. Ann., 248 (1980), 73-77
H. Komiya, coincidence theorem and saddle point theorem, proc. Amer. Math. soc. , 96 (1986), 599 – 602
E. Tarafdar, X. Z. Yuan, A remark on coincidence theorems , proc. Amer .soc., 122 (3) (1994), 957 -959
E. Tarafdar, P. J. Watson, A coincidence point theorem and related results, Appl. Math .let., 11 (1) (1998), 37 - 40
H. J. Zhang, Minimax Inequalities of Key Fan, Apple math. soc , 99 (1987), 980 - 682