Coincidence theorem and saddle point theorem

Author:
H. Komiya

Journal:
Proc. Amer. Math. Soc. **96** (1986), 599-602

MSC:
Primary 47H10; Secondary 49A40, 54H25

DOI:
https://doi.org/10.1090/S0002-9939-1986-0826487-0

MathSciNet review:
826487

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Abstract | References | Similar Articles | Additional Information

Abstract: We discuss Browder's coincidence theorem and derive a saddle point theorem from it.

**[1]**F. E. Browder,*The fixed point theory of multi-valued mappings in topological vector spaces*, Math. Ann.**177**(1968), 283-301. MR**0229101 (37:4679)****[2]**-,*Coincidence theorems, minimax theorems and variational inequalities*, Contemporary Math., Vol. 26, Amer. Math. Soc., Providence, R.I., 1984, pp. 67-80. MR**737389 (85k:47099)****[3]**N. Dunford and J. T. Schwartz,*Linear operators*, Part I, Wiley, New York, 1971. MR**1009162 (90g:47001a)****[4]**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)****[5]**-,*A generalization of Tychonoff's fixed point theorem*, Math. Ann.**142**(1961), 305-310.**[6]**-,*Extensions of two fixed point theorems of F. E. Browder*, Math. Z.**112**(1969), 234-240. MR**0251603 (40:4830)****[7]**C. W. Ha,*Minimax and fixed point theorems*, Math. Ann.**248**(1980), 73-77. MR**569411 (81i:47058)****[8]**S. Kakutani,*A generalization of Brouwer's fixed-point theorem*, Duke Math. J.**8**(1941), 457-459. MR**0004776 (3:60c)****[9]**J. L. Kelly and I. Namioka,*Linear topological spaces*, Springer, New York, 1976. MR**0394084 (52:14890)****[10]**S. Simons,*Two-function minimax theorems and variational inequalities for functions on compact and noncompact sets, with some comments on fixed-point theorems*, Proc. 1983 Amer. Math. Soc. Summer Inst. on Nonlinear Funct. Anal.; Proc. Sympos. Pure Math. (to appear). MR**843623 (87h:49019)****[11]**W. Takahashi,*Nonlinear variational inequalities and fixed point theorems*, J. Math. Soc. Japan**28**(1976), 168-181. MR**0399979 (53:3817)****[12]**-,*Recent results in fixed point theory*, Southeast Asian Bull. Math.**4**(1980), 59-85. MR**655748 (83f:47046)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1986-0826487-0

Keywords:
Coincidence theorem,
saddle point,
fixed point

Article copyright:
© Copyright 1986
American Mathematical Society