Abstract
In this paper, we establish the existence of a fixed point for generalized nonexpansive multivalued mappings in hyperbolic spaces and we prove some Delta -convergence and strong convergence theorems for the iterative scheme proposed by Chang et al. (Appl Math Comp 249:535–540, 2014) to approximate a fixed point for generalized nonexpansive multivalued mapping under suitable conditions. Our results are the extension and improvements of the recent well-known results announced in the current literature.
Highlights
The study of fixed points for multivalued contractions and nonexpansive mappings using the Hausdorff metric was initiated by Markin (1973) and Nadler (1969)
The existence of fixed points for multivalued nonexpansive mappings in convex metric spaces has been shown by Shimizu and Takahashi (1996), that is, they proved that every multivalued mapping T : X → C(X) has a fixed point in a bounded, complete and uniformly convex metric space (X, d), where C(X) is the family of all compact subsets of X
We provide an example of generalized nonexpansive multivalued mapping satisfying condition (C ) and (E)
Summary
The study of fixed points for multivalued contractions and nonexpansive mappings using the Hausdorff metric was initiated by Markin (1973) and Nadler (1969). Since many authors have been published papers on the existence and convergence of fixed points for multivalued nonexpansive mappings in uniformly convex Banach spaces and convex metric spaces. Different iterative algorithms have been used to approximate the fixed points of multivalued nonexpansive mappings (see Abbas et al 2011; Khan and Yildirim 2012; Khan et al 2010; Panyanak 2007; Shahzad and Zegeye 2009; Sastry and Babu 2005; Song and Wang 2008, 2009; Song and Cho 2011) in uniformly convex Banach spaces
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