One-local retracts and Banach operator pairs in metric spaces

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Hussain N, Khamsi MA, Kirk WA. One-local retracts and banach operator pairs in metric spaces. Applied Mathematics and Computation 2012 15 June 2012;218(20):10072-81.


In this paper, we first introduce the concept of NR-map and then use this concept to establish the existence of common fixed points for Banach operator pairs in the context of uniformly convex geodesic metric spaces. New proofs of main results (Theorems 2.1 and 3.5) of Chen and Li [J. Chen, Z. Li, Banach operator pair and common fixed points for nonexpansive maps, Nonlinear Anal. 74 (2011) 3086–3090] are presented. Further, we prove De Marr’s theorem for the family of symmetric Banach operator pairs in metric spaces and R-trees for single and multivalued mappings satisfying conditions that generalize the concept of nonexpansivity.