An extended local principle of fixed points for weakly contractive set-valued mappings. (4th May 2022)

• Record Type: Journal Article
• Authors: Mansour, M. Ait; Bekkali, A. El; Lahrache, J.
• Is Part Of: Optimization. Volume 71:Number 5(2022)
• Page Start: 1409
• Page End: 1420
• Publication Date: 2022-05-04
• Subjects: Fixed point -- local contraction mapping principle -- Nadler fixed point theorem -- fixed point assertions; 47H10 -- 54H25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.2009829
• Languages: English
• ISSNs: 0233-1934

Abstract

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.