Convergence Analysis for a Three-Step Thakur Iteration for Suzuki-Type Nonexpansive Mappings with Visualization

Abstract

The class of Suzuki mappings is reanalyzed in connection with a three-steps Thakur procedure. The setting is provided by a uniformly convex Banach space, that is normed space endowed with some symmetric geometric properties and some topological properties. Once more, the fact that property ( C ) holds on as a generalized nonexpansiveness condition is emphasized throughout some examples. One example uses the setting of R 2 with the Taxicab norm. It is further included in a numerical experiment in connection with seven iteration procedures, resulting a visual analysis of convergence.

Fixed-Point Convergence Results of a Three-Step Iterative Process in CAT(0) Spaces

“…e aim of this research work is to improve and extend the main outcome of Usurelu et al [23] to the nonlinear setting of CAT(0) spaces. Simultaneously, our results improve and extend the corresponding results of akur et al [21] and Usurelu and Postolache [22]. Moreover, we suggest a new example of Garcia-Falset maps which exceeds the corresponding class of Suzuki maps and prove that its Sahu-akur iterative process (3) is more effective than the many other iterative schemes.…”

“…In [21], akur et al established many interesting weak and strong convergence results for the class of nonexpansive maps under iterative process (3) in the ground setting of Banach spaces. Recently in 2019, Usurelu and Postolache [22] improved and extended the main outcome of akur et al [21] to the larger class of Suzuki maps. Very recently in 2020, Usurelu et al [23] quickly improved and extended the main outcome of Usurelu and Postolache [22] to the general setting of Garcia-Falset maps.…”

“…Recently in 2019, Usurelu and Postolache [22] improved and extended the main outcome of akur et al [21] to the larger class of Suzuki maps. Very recently in 2020, Usurelu et al [23] quickly improved and extended the main outcome of Usurelu and Postolache [22] to the general setting of Garcia-Falset maps. e aim of this research work is to improve and extend the main outcome of Usurelu et al [23] to the nonlinear setting of CAT(0) spaces.…”

On Iteration Sn for Operators with Condition (D)

“…This time, the procedure was connected to Suzuki-type mappings. Similar approaches involving other iteration procedures were recently performed in [10,11].…”

Iterative algorithms of common solutions for a hierarchical fixed point problem, a system of variational inequalities, and a split equilibrium problem in Hilbert spaces

“…In view of these different three kinds of problems, there are some new research results on numerical algorithm in the recent literature. Under the setting of uniformly convex Banach spaces, in [27][28][29][30], the Thakur three-step iterative process in the context of Suzukitype nonexpansive mappings or generalized nonexpansive mappings enriched with property (E) was studied, and a comparative numerical experiment was performed with the visualization of some convergence behaviors. In [25], an S-iteration technique for finding common fixed points for nonself quasi-nonexpansive mappings was developed, and convergence properties of the proposed algorithm were analyzed.…”