Fixed-Point Convergence of Multi-Valued Non-Expansive Mappings with Applications

Abstract

This paper is dedicated to the advancement of fixed-point results for multi-valued asymptotically non-expansive maps regarding convergence criteria in complete uniformly convex hyperbolic metric spaces that are endowed with a graph. The famous fixed-point theorems of Goebel and Kirk, Khamsi and Khan, along with other recent results in the literature can be obtained as corollaries of these main results. A nice graph and an interesting example are also provided in support of the hypothesis of the main results.

Keywords

• G -asymptotically non-expansive mapping%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <named-content content-type="inline-formula"><inline-formula> <mml:math id="mm216000"> <mml:semantics> <mml:mi mathvariant="fraktur">G</mml:mi> </mml:semantics> </mml:math> </inline-formula></named-content>-asymptotically non-expansive mapping
• uniformly convex hyperbolic metric space
• Mann iteration process
• multi-valued mapping
• directed graphs