Document Type : Research Paper

Author

• Mohammad Moosaei

Department of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, Iran

Abstract

We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the fixed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and convex, then its the fixed points set is nonempty, closed and convex.

Keywords

• Fixed point
• fundamentally nonexpansive mappings
• nonexpansive mappings
• Opial's condition
• uniformly convex Banach spaces