Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Coincidence theorem and saddle point theorem

Author: H. Komiya
Journal: Proc. Amer. Math. Soc. 96 (1986), 599-602
MSC: Primary 47H10; Secondary 49A40, 54H25
MathSciNet review: 826487
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

References [Enhancements On Off] (What's this?)

  • [1] Felix E. Browder, The fixed point theory of multi-valued mappings in topological vector spaces, Math. Ann. 177 (1968), 283–301. MR 0229101
  • [2] Felix E. Browder, Coincidence theorems, minimax theorems, and variational inequalities, Conference in modern analysis and probability (New Haven, Conn., 1982), Contemp. Math., vol. 26, Amer. Math. Soc., Providence, RI, 1984, pp. 67–80. MR 737389, 10.1090/conm/026/737389
  • [3] Nelson Dunford and Jacob T. Schwartz, Linear operators. Part I, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1988. General theory; With the assistance of William G. Bade and Robert G. Bartle; Reprint of the 1958 original; A Wiley-Interscience Publication. MR 1009162
  • [4] Ky. 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
  • [5] -, A generalization of Tychonoff's fixed point theorem, Math. Ann. 142 (1961), 305-310.
  • [6] Ky Fan, Extensions of two fixed point theorems of F. E. Browder, Math. Z. 112 (1969), 234–240. MR 0251603
  • [7] Chung Wei Ha, Minimax and fixed point theorems, Math. Ann. 248 (1980), no. 1, 73–77. MR 569411, 10.1007/BF01349255
  • [8] Shizuo Kakutani, A generalization of Brouwer’s fixed point theorem, Duke Math. J. 8 (1941), 457–459. MR 0004776
  • [9] John L. Kelley and Isaac Namioka, Linear topological spaces, Springer-Verlag, New York-Heidelberg, 1976. With the collaboration of W. F. Donoghue, Jr., Kenneth R. Lucas, B. J. Pettis, Ebbe Thue Poulsen, G. Baley Price, Wendy Robertson, W. R. Scott, and Kennan T. Smith; Second corrected printing; Graduate Texts in Mathematics, No. 36. MR 0394084
  • [10] S. Simons, Two-function minimax theorems and variational inequalities for functions on compact and noncompact sets, with some comments on fixed-point theorems, Nonlinear functional analysis and its applications, Part 2 (Berkeley, Calif., 1983) Proc. Sympos. Pure Math., vol. 45, Amer. Math. Soc., Providence, RI, 1986, pp. 377–392. MR 843623
  • [11] Wataru Takahashi, Nonlinear variational inequalities and fixed point theorems, J. Math. Soc. Japan 28 (1976), no. 1, 168–181. MR 0399979
  • [12] Wataru Takahashi, Recent results in fixed point theory, Southeast Asian Bull. Math. 4 (1980), no. 2, 59–85. MR 655748

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47H10, 49A40, 54H25

Retrieve articles in all journals with MSC: 47H10, 49A40, 54H25

Additional Information

Keywords: Coincidence theorem, saddle point, fixed point
Article copyright: © Copyright 1986 American Mathematical Society