Abstract
In this paper some new types of KKM theorem and section theorems are given. As applications, the existence problems of solutions for three kinds of variational inequalities and fixed point problem for set-valued mapping have been studied by using those results. The results presented in this paper improve and extend the main results in [1–19].
Similar content being viewed by others
References
Bardaro, C. and R. Ceppitelli, Some further generalizations of Knaster-Kuratowski-Mazurkiewicz theorem and minimax inequalities.J. Math. Anal. Appl.,132 (1988), 484–490.
Bardaro, C. and R. Ceppitelli, Applications of generalized Knaster-Kuratowski-Mazukiewicz theorem to variational inequalites,J. Math. Anal. Appl.,137 (1989), 46–58.
Bardaro, C. and R. Ceppitelli, Fixed point theorems and vector-valued minimax theorems,J. Math. Anal. Appl.,146 (1990), 363–373.
Browder, F. E., A new generalization of the Schauder fixed point theorem,Math. Ann.,174 (1967), 285–290.
Browder, F. E., The fixed point theory of multi-valued mappings in topological vector space,Math. Ann.,177 (1968), 283–301.
Chang Shih-sen and Ma Yi-hai, Generalized KKM theorem on H-space with applications,J. Math. Anal. Appl.,163 (1992), 406–421.
Chang Shih-sen and Zhang Ying, Generalized KKM theorem and variational inequalities,J. Math. Anal. Appl.,159 (1991), 208–223.
Fan, K., A minimax inequality and applications,Inequalities III, Ed. by O. Shisha, Academic Press, New York (1972), 103–113.
Fan, K, Fixed point and related theorems for noncompact convex sets,Game Theory and Releated Topics. Eds. by O. Moeschlin and D. Pallaschke, North-Holland (1979), 151–156.
Fan, K., Some properties of convex of convex set related to fixed point theorems,Math. Ann.,266 (1984), 519–537.
Ko, H. M. and K. K. Tan, A coincidence theorem with application to minimax inequalities and fixed point theorems,Tamkang J. Math.,17 (1986), 37–43.
Lassonde, M., On the use of KKM multifunctions in fixed point theory and related topics,J. Math. Anal. Appl.,97 (1983), 151–201.
Park, S., Generalizations of Ky Fan's Matching theorems and their applications,J. Math. Anal. Appl.,141 (1989), 164–176.
Shih, M. H. and K. K. Tan, A geometric property of convex sets with applications to minimax type inequalities and fixed point theorems,J. Austral. Math. Soc., Series A.,45 (1988), 169–183.
Shih, M. H. and K. K. Tan, The Ky Fan minimax principle, sets with convex sections and variational inequalities,Differential Geometry-Calculus of Variational and Their Applications, Eds. by M. Rassias and T. Rassia, New York (1985), 471–481.
Takahashi, W., Fixed point minimax and Hahu-Banach theorems,Proc. Sympos. Pure Math.,45, Part 2 (1986), 419–427.
Tan, K. K., Comparison theorems on minimax inequalities, variational inequalities and fixed point theorems,J. London Math. Soc.,23 (1983), 555–562.
Yen, C. L., A minimax inequality and its applications to variational inequalities,Pacific J. Math.,97 (1981), 477–481.
Gwinner, J., On some fixed points and variational inequalities—A circular tour.Nonlinear Anal.,5, 5 (1981), 565–583.
Author information
Authors and Affiliations
Additional information
Project supported by the National Natural Science Foundation of China First Received Sept. 1, 1993
Rights and permissions
About this article
Cite this article
Shi-sheng, Z., Xian, W. Topological version of section theorems with applications. Appl Math Mech 16, 133–142 (1995). https://doi.org/10.1007/BF02451453
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02451453