Abstract
We study the existence of fixed points and convergence of iterates for asymptotic pointwise contractions in uniformly convex metric spaces. We also study the existence of fixed points for set-valued nonexpansive mappings in the same class of spaces. Our results do not assume convexity of the metric which makes a big difference when studying the existence of fixed points for set-valued mappings.
Highlights
This paper is motivated by the recent paper 1
We study the existence of fixed points and convergence of iterates for asymptotic pointwise contractions in uniformly convex metric spaces
We study the existence of fixed points for setvalued nonexpansive mappings in the same class of spaces
Summary
This paper is motivated by the recent paper 1. In 1 the authors study different questions related to fixed points of asymptotic pointwise contractive/nonexpansive mappings in CAT 0 spaces. The notion of asymptotic pointwise contractions was introduced in 6 It was studied in 7 where, by means of ultrapower techniques, different results about the. Finding fixed point for set-valued nonexpansive mappings in uniformly convex metric spaces was first studied by Shimizu and Takahashi 9 , where the existence of fixed points was guaranteed under stronger conditions on the modulus of convexity and the additional condition of metric convexity of the space. The fact that we do not have that the metric are convex will make the problem more complicated and this will take us to impose new conditions on the modulus of convexity which we will relate with the geometry of the space
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.
