One-Step Iteration Scheme for Multivalued Nonexpansive Mappings in CAT(0) Spaces

Common fixed point iterations for a class of multi-valued mappings in $$\mathbf {CAT}(0)$$ spaces

“…In this paper, we prove some convergence theorems for a finite family of multi-valued generalized nonexpansive mappings using scheme (2.4). Our results generalize the corresponding results in [1,26] and references cited therein.…”

“…The following statements are quoted from [26]: "Sastry and Babu [21] showed that under certain conditions, Mann and Ishikawa iterative algorithms for a multi-valued nonexpansive mapping with a fixed point x converge to a fixed point y of the mapping. Panyanak [18] extended their results to a uniformly convex Banach space.…”

“…Abbas et al [1] proposed a one-step iterative scheme to find a common fixed point of two multi-valued nonexpansive mappings in a uniformly convex Banach space. Recently, Uddin et al [26] discovered a few gaps in the scheme proposed in [1] and came up with a new one-step iterative scheme for fixed points of two multi-valued nonexpansive mappings in C AT (0) space and removed the gaps found in [1]".…”

“…Motivated by [1,26], we recommend a new scheme to approximate common fixed point(s) of a finite family of generalized multi-valued nonexpansive mappings in C AT (0) spaces.…”

Proximal point algorithms involving Cesàro type mean of total asymptotically nonexpansive mappings in CAT(0) spaces

“…Proof. With the help of (24)- (25) and 27 Next we prove that {x n } is a Cauchy sequence in C. In fact, it follows from (12) that for any q ∈ Ω, we have that By taking inf p∈Ω on both sides of (28), we obtain that…”