On a minimax inequality of Ky Fan

Author:
Chung Wei Ha

Journal:
Proc. Amer. Math. Soc. **99** (1987), 680-682

MSC:
Primary 47H10; Secondary 49A29, 49A40, 90C48

DOI:
https://doi.org/10.1090/S0002-9939-1987-0877039-9

MathSciNet review:
877039

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Abstract | References | Similar Articles | Additional Information

Abstract: An extension of a minimax inequality of Ky Fan is given. It is then used to generalize to the set-valued setting a fixed point theorem of Ky Fan.

**[1]**J. P. Aubin,*Mathematical methods of game and economic theory*, North-Holland, Amsterdam, 1979. MR**556865 (83a:90005)****[2]**K. Fan,*Fixed-point and minimax theorems in locally convex topological linear spaces*, Proc. Nat. Acad. Sci. U.S.A.**38**(1952), 121-126. MR**0047317 (13:858d)****[3]**K. Fan,*Extensions of two fixed point theorems of F. E. Browder*, Math. Z.**112**(1969), 234-240. MR**0251603 (40:4830)****[4]**K. Fan,*A minimax inequality and applications*, Inequalities, vol. III, Academic Press, New York and London, 1972, pp. 103-113. MR**0341029 (49:5779)****[5]**K. Fan,*Some properties of convex sets realted to fixed point theorems*, Math. Ann**266**(1984), 519-537. MR**735533 (85i:47060)****[6]**C.-W. Ha,*Minimax and fixed point theorems*, Math. Ann.**248**(1980), 73-77. MR**569411 (81i:47058)****[7]**S. Reich,*Fixed points in locally convex spaces*, Math. Z.**125**(1972), 17-31. MR**0306989 (46:6110)**

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DOI:
https://doi.org/10.1090/S0002-9939-1987-0877039-9

Article copyright:
© Copyright 1987
American Mathematical Society