Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-17T00:17:17.419Z Has data issue: false hasContentIssue false
  • English
  • Français

Some generalizations in H-modular spaces of Fan's best approximation theorem

Part of: Nonlinear operators and their properties Connections with other structures, applications

Published online by Cambridge University Press:  09 April 2009

Carlo Bardaro  and
Rita Ceppitelli
Carlo Bardaro
Affiliation:
Dipartimento di Matematica, Università degli Studi di Perugia, via Pascoli, 06100 Perugia, Italy
Rita Ceppitelli
Affiliation:
Dipartimento di Mathematica e Fisica, Università di Camerino, via Venanzi 16, 62032 Camerino (MC), Italy
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.

We state best approximation and fixed point theorems in modular spaces endowed with an H-space structure given by the modular topology. We consider both the cases of single valued functions and multifunctions. These theorems extend some previous results due to Ky Fan.

MSC classification

Secondary: 47H10: Fixed-point theorems 54H25: Fixed-point and coincidence theorems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 56 , Issue 3 , June 1994 , pp. 291 - 302
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Bardaro, C. and Ceppitelli, R., ‘Minimax inequalities in Riesz spaces’, Atti. Sem. Mat. Fis. Univ. Modena 35 (1987), 63–70.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]Bardaro, C. and Ceppitelli, R., ‘Applications of the generalized Knaster-Kuratowski-Mazurkiewicz Theorem to variational inequalities’, J. Math. Anal. Appl. 137 (1989), 46–58.CrossRefGoogle Scholar
[4]Bardaro, C. and Ceppitelli, R., ‘Fixed point theorems and vector valued minimax theorems’, J. Math. Anal. Appl. 146 (1990), 363–373.CrossRefGoogle Scholar
[5]Browder, F. E., ‘A new generalization of the Schauder fixed point theorem’, Math. Ann. 174 (1967), 285–290.CrossRefGoogle Scholar
s[6]Castaing, C. and Valadier, M., Convex analysis and measurable multifunctions, Lecture Notes in Math. 580 (Springer, Berlin, 1977).CrossRefGoogle Scholar
[7]Chen, G. Y., ‘Generalized section theorem and minimax inequality for a vector-valued mapping’, to appear.Google Scholar
[8]Fan, K., ‘Extensions of two fixed point theorems of F. E. Browder’, Math. Z. 112 (1969), 234–240.CrossRefGoogle Scholar
[9]Horvath, C. D., ‘Points fixes et coincidences dans les éspaces topologiques compacts contractiles’, C. R. Acad. Sci. Paris Sér. I Math. 299 (1984), 519–521.Google Scholar
[10]Horvath, C. D., Some results on multivalued mappings and inequalities without convexity, Lecture Notes in Pure and Appl. Math. 107 (Marcel Dekker, New York, 1988).Google Scholar
[11]Horvath, C. D., ‘Contractibility and generalized convexity’, J. Math. Anal. Appl. 156 (1991), 341–357.CrossRefGoogle Scholar
[12]Kozlowski, W. M., Modular function spaces (Marcel Dekker, New York, 1989).Google Scholar
[13]Lassonde, M., ‘On the use of K.K.M. multifunctions in fixed point theory and related topics’, J. Math. Anal. Appl. 97 (1983), 151–201.CrossRefGoogle Scholar
[14]Musielak, J., Orlicz spaces and modular spaces, Lecture Notes in Math. 1034 (Springer, Berlin, 1983).CrossRefGoogle Scholar
[15]Sehgal, V. M. and Singh, S. P., ‘A generalization to multifunctions of Fan's best approximation theorem’, Proc. Amer. Math. Soc. 102 (1988), 534–537.Google Scholar