On fixed points of fundamentally nonexpansive mappings in Banach spaces

Document Type : Research Paper


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


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.


Volume 7, Issue 1 - Serial Number 1
January 2016
Pages 219-224
  • Receive Date: 28 January 2015
  • Revise Date: 08 August 2015
  • Accept Date: 04 September 2015