The Chebyshev selections and fixed points of set-valued mappings in Banach spaces with some uniform convexity

Authors:
Jian-Zhong Xiao;Xing-Hua Zhu
Affiliations:
-;-
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2011

Citing 2
Cited 0

Sadovskii's fixed point theorem without convexity

Nonlinear Analysis: Theory, Methods & Applications
Perturbation of Sets and Centers

Journal of Global Optimization

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Abstract

The existence of a continuous Chebyshev selection for a Hausdorff continuous set-valued mapping is studied in a Banach space with some uniform convexity. As applications, some existence results of Chebyshev fixed point for condensing set-valued mappings are given, and the existence of Chebyshev solutions for an integral inclusion is proved.