Some stability and strong convergence results for the algorithm with perturbations for a T-Ciric quasicontraction in CAT(0) spaces
Fecha de publicación: 10/03/2023

In this paper, we establish the stability and strong convergence theorems, for the three-step iteration with perturbations for a T-Ciric quasicontraction, in the environment of the CAT(0) space. Finally, an application to the integral-type contraction and an example are shown.

Approximating Fixed Points of Suzuki (α,β) -Nonexpansive Mappings in Ordered Hyperbolic Metric Spaces
Fecha de publicación: 04/05/2021

In this chapter, we define the class of monotone (α,β)-nonexpansive mappings and prove that they have an approximate fixed point sequence in partially ordered hyperbolic metric spaces. We prove the Δ and strong convergence of the CR-iteration scheme.

Perturbed approximations of fixed points of nonexpansive mappings in CAT_p(0) spaces
Fecha de publicación: 20/01/2021

Using the concept of the spaces proposed by Khamsi et al. [Khamsi, M. A. and Shukri, S. A., Generalized spaces. Bull. Belg. Math. Soc. Simon Stevin,  24 (2017), No. 3, 417–426], we establish -convergence and strong convergence of a perturbed variant of Agarwal et al. -iteration process for nonexpansive mapping. Finally, from them we deduce results valid for -nonexpansive mappings.

Hybrid algorithm with perturbations for total asymptotically non-expansive mappings in CAT(0) space
Fecha de publicación: 27/05/2019

In this paper, we establish strong and Δ-convergence theorems of the modified hybrid-CR three steps iteration with perturbations for total asymptotically non-expansive mapping in CAT(0) spaces. Our results improve and extend the corresponding results from the current literature. We also provide three examples to illustrate the convergence behaviour of the proposed algorithm and numerically compare the convergence of the proposed iteration scheme with the existing schemes.