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A set-valued generalization of Ricceri’s theorem related to Fan-Takahashi minimax inequality. (English) Zbl 1347.49030

Summary: In this paper, we propose a Ricceri type theorem on the Fan-Takahashi minimax inequality for set-valued maps by using the scalarization method proposed by Kuwano, Tanaka and Yamada based on a certain type of set-relations.

MSC:

49J53 Set-valued and variational analysis
49J35 Existence of solutions for minimax problems
54C60 Set-valued maps in general topology
90C29 Multi-objective and goal programming
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Full Text: Euclid

References:

[1] K. Fan, A minimax inequality and its applications , in Inequalities III, O. Shisha (ed.), Academic Press, New York, 1972, pp.103-113.
[2] D. Kuroiwa, T. Tanaka and T. X. D. Ha, On Cone Convexity of Set-Valued Maps , Nonlinear Anal. 30 (1997), 1487-1496. · Zbl 0895.26010
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[9] Y. Sonda, I. Kuwano and T. Tanaka, Cone Semicontinuity of Set-Valued Maps by Analogy with Real-Valued Semicontinuity , Nihonkai Math. J. 21 (2010), 91-103. · Zbl 1217.49021
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