Abstract
In this paper we prove Leray-Schauder and Furi-Pera types fixed point theorems for a class of multi-valued mappings with weakly sequentially closed graph. Our results improve and extend previous results for weakly sequentially closed maps and are very important in applications, mainly for the investigating of boundary value problems on noncompact intervals.
Highlights
In this paper we prove Leray-Schauder and Furi-Pera types fixed point theorems for a class of multi-valued mappings with weakly sequentially closed graph
Fixed point theory for weakly completely continuous multi-valued mappings takes an important role for the existence of solutions for operator inclusions, positive solutions of elliptic equation with discontinuous nonlinearities and periodic and boundary value problems for second order differential inclusions and others
The aim of the present paper is to extend and improve these theorems to the case of weakly condensing and 1-set weakly contractive multi-valued maps with weakly sequentially closed graph
Summary
Fixed point theory for weakly completely continuous multi-valued mappings takes an important role for the existence of solutions for operator inclusions, positive solutions of elliptic equation with discontinuous nonlinearities and periodic and boundary value problems for second order differential inclusions (see [1,2,3]) and others. In [4] O’Regan has proved a number of fixed point theorems for multi-valued maps defined on bounded domains with weakly compact convex values and which are weakly contractive and have weakly sequentially closed graph. The aim of the present paper is to extend and improve these theorems to the case of weakly condensing and 1-set weakly contractive multi-valued maps with weakly sequentially closed graph. Let Z a non-empty subset of a Banach space Y and F : Z 2X be a multi-valued mapping. The notion above is a generalization of the important well known DeBlasi measure of weak non-compactness (see [11]) defined on each bounded set of E by. Let F : Pcl,cv be an upper semicontinuous multi-valued mapping such that F is relatively compact.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
