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Signal recovery and polynomiographic visualization of modified Noor iteration of operators with property (E)

Paimsang Papinwich, Thianwan Tanakit

Demonstratio Mathematica

2024

Vol. 57, nr 1

art. no. 20240070

This article aims to provide a modified Noor iterative scheme to approximate the fixed points of generalized nonexpansive mappings with property (E) called MN-iteration. We establish the strong and weak convergence results in a uniformly convex Banach space. Additionally, numerical experiments of the iterative technique are demonstrated using a signal recovery application in a compressed sensing situation. Ultimately, an illustrative analysis regarding Noor, SP-, and MN-iteration procedures is obtained via polysomnographic techniques. The images obtained are called polynomiographs. Polynomiographs have importance for both the art and science aspects. The obtained graphs describe the pattern of complex polynomials and also the convergence properties of the iterative method. They can also be used to increase the functionality of the existing polynomiography software.

Mixed-type SP-iteration for asymptotically nonexpansive mappings in hyperbolic spaces

Paimsang Papinwich, Thianwan Tanakit

Demonstratio Mathematica

2023

Vol. 56, nr 1

art. no. 20230113

In this article, we introduce and study some strong convergence theorems for a mixed-type SP-iteration for three asymptotically nonexpansive self-mappings and three asymptotically nonexpansive nonself-mappings in uniformly convex hyperbolic spaces. In addition to that, we provide an illustrative example. The findings here expand and improve upon some of the relevant conclusions found in the published literature.