An extended local principle of fixed points for weakly contractive set-valued mappings

Abstract

In this paper, we establish an extension of the well-known Contraction Mapping Principle for Set-Valued Mappings. We consider a larger class of weakly contractive mappings, which allows us to cover, extend and unify many assertions of fixed point theory. As an application, we derive two quantitative stability results for fixed points of weakly contractive maps.

Keywords:

• Fixed point
• local contraction mapping principle
• Nadler fixed point theorem
• fixed point assertions

2010 AMS:

• 47H10
• 54H25

Acknowledgments

The authors wish to thank an anonymous referee as well as an associate editor for nice suggestions to improve the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).