Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-22T04:25:33.171Z Has data issue: false hasContentIssue false
  • English
  • Français

Some coincidence theorems and applications

Published online by Cambridge University Press:  17 April 2009

Xie Ping Ding  and
E. Tarafdar
Xie Ping Ding
Affiliation:
Department of Mathematics SichunnNormal University Chengdu, SichuanPeople's Republic of China610066
E. Tarafdar
Affiliation:
Department of MathematicsThe University of QueenslandQueensland 4072, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, we establish a new coincidence theorem for a Browder type set-valued mapping and an upper semi-continuous set-valued mapping with compact acyclic values in an H-space which generalises some recent results in the literature. As applications we obtain two H a type coincidence theorems and existence theorems of maximal elements for preference correspondences.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 50 , Issue 1 , August 1994 , pp. 73 - 80
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Aubin, J.P. and Ekeland, I., Applied Nonlinear Analysis (John Wiley and Sons, New York, 1984).Google Scholar
[2]Bardaro, C. and Ceppitelli, R., ‘Some further generalizations of Knaster-Kuratowski-Mazurkiewicz theorem and minimax inequalities’, J. Math. Anal. Appl. 132 (1988), 484–490.CrossRefGoogle Scholar
[3]Borglin, A. and Keiding, H., ‘Existence of equilibrium actions of equilibrium, A note on the ‘new’ existence theorems’, J. Math. Econom. 3 (1976), 313–316.CrossRefGoogle Scholar
[4]Browder, F.E., ‘Coincidence theorems, manimax theorems, and variational inequalities’, Contemp. Math. 26 (1984), 47–80.Google Scholar
[5]Ding, X.P., ‘New generalizations of an H-KKM type theorem and their applications’, Bull. Austral. Math. Soc. 48 (1993), 451–464.CrossRefGoogle Scholar
[6]Ding, X.P. and Tan, K.K., ‘Matching theorems, fixed point theorems and minimax inequalities without convexity’, J. Austral. Math. Soc. Ser. A 49 (1990), 111–128.CrossRefGoogle Scholar
[7]Ding, X.P. and Tan, K.K., ‘Fixed point theorems and equilibria of noncompact generalized games’, in Fixed point theory and applications, (Tan, K.K., Editor) (World Sci. Press, Singapore, London, 1992), pp. 80–96.Google Scholar
[8]Ding, X.P. and Tan, K.K., ‘On equilibria of non-compact generalized games’, J. Math. Anal. Appl. 177 (1993), 226–238.CrossRefGoogle Scholar
[9]Fan, Ky, ‘Fixed-point and minimax theorems in locally convex topological linear spaces’, Proc. Nat. Acad. Sci. USA 38 (1952), 121–126.CrossRefGoogle ScholarPubMed
[10]Fan, Ky, ‘A generalization of Tychonoff's fixed point theorem’, Math. Ann. 142 (1961), 305–310.CrossRefGoogle Scholar
[11]Ha, C.W., ‘Extensions of two fixed point theorems of Ky Fan’, Math. Z. 190 (1985), 13–16.CrossRefGoogle Scholar
[12]Horvath, C., ‘Some results on multivalued mappings and inequalities without convexity’, in Nonlinear and convex analysis, (Lin, B.L. and Simons, S., Editors) (Marcel Dekker, 1987), pp. 99–106.Google Scholar
[13]Komiya, H., ‘Coincidence theorems and Saddle point theorem’, Proc. Amer. Math. Soc. 96 (1986), 59–602.CrossRefGoogle Scholar
[14]Mehta, G. and Sessa, S., ‘Coincidence theorems and maximal elements in topological vector spaces’, Math. Japan. 47 (1992), 839–845.Google Scholar
[15]Park, S., ‘Some coincidence theorems on acyclic multifunctions and applications to KKM theory’, in Fixed point theory and applications, (Tan, K.K., Editor) (World Sci. Press, Singapore, London, 1992), pp. 248–277.Google Scholar
[16]Sessa, S., ‘Some remarks and applications of an extensions of a lemma of Ky Fan’, Comment. Math. Univ. Carolin. 29 (1988), 567–575.Google Scholar
[17]Shioji, N., ‘A further generalization of Knaster-Kuratowski-Mazurkiewcz theorem’, Proc. Amer. Math. Soc. 111 (1991), 187–195.CrossRefGoogle Scholar
[18]Tarafdar, E., ‘On nonlinear variational inequalities’, Proc. Amer. Math. Soc. 67 (1977), 95–98.CrossRefGoogle Scholar
[19]Tarafdar, E., ‘A fixed point theorem in H-space and related results’, Bull. Austral. Math. Soc. 42 (1990), 133–140.CrossRefGoogle Scholar
[20]Tarafdar, E., ‘A Fixed point theorems and equilibrium point of an abstract economy’, J. Math. Econom. 20 (1991), 211–218.CrossRefGoogle Scholar
[21]Tarafdar, E., ‘Fixed point theorems in H-spaces and equilibrium points of abstract economies’, J. Austral Math. Soc. Ser. A 53 (1992), 252–260.CrossRefGoogle Scholar
[22]Yannelis, N.C. and Prabhakar, N.D., ‘Existence of maximal elements and equilibrium in linear topological spaces’, J. Math. Econom. 12 (1983), 233–245.CrossRefGoogle Scholar