Approximation theorems for G-nonexpansive mappings in convex metric spaces by three step iterations

Muhammad Nouman Aslam Khan; Maliha Rashid; Amna Kalsoom; Naeem Saleem; Madeeha; Manuel De La Sen

doi:10.1016/j.aej.2024.05.067

Approximation theorems for G-nonexpansive mappings in convex metric spaces by three step iterations

Muhammad Nouman Aslam Khan, Maliha Rashid, Amna Kalsoom, Naeem Saleem^*, Madeeha, Manuel De La Sen

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

In this article, we study the convergence behavior of G-nonexpansive mappings for three-step iterations in convex metric space along with the directed graph. We demonstrate the Δ-convergence as well as the strong convergence results for these mappings. For supporting our main results we presented a numerical example and convergence comparison of modified Thianwan iteration with SP iteration scheme and Noor iteration scheme.

Original language	English
Pages (from-to)	1-9
Number of pages	9
Journal	Alexandria Engineering Journal
Volume	102
DOIs	https://doi.org/10.1016/j.aej.2024.05.067
Publication status	Published - Sept 2024
Externally published	Yes

Keywords

Convex metric spaces
Directed graph
Δ-convergence as well as strong convergence

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10.1016/j.aej.2024.05.067

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title = "Approximation theorems for G-nonexpansive mappings in convex metric spaces by three step iterations",

abstract = "In this article, we study the convergence behavior of G-nonexpansive mappings for three-step iterations in convex metric space along with the directed graph. We demonstrate the Δ-convergence as well as the strong convergence results for these mappings. For supporting our main results we presented a numerical example and convergence comparison of modified Thianwan iteration with SP iteration scheme and Noor iteration scheme.",

keywords = "Convex metric spaces, Directed graph, Δ-convergence as well as strong convergence",

author = "Khan, {Muhammad Nouman Aslam} and Maliha Rashid and Amna Kalsoom and Naeem Saleem and Madeeha and {De La Sen}, Manuel",

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AU - Khan, Muhammad Nouman Aslam

AU - Rashid, Maliha

AU - Kalsoom, Amna

AU - Saleem, Naeem

AU - Madeeha,

AU - De La Sen, Manuel

PY - 2024/9

Y1 - 2024/9

N2 - In this article, we study the convergence behavior of G-nonexpansive mappings for three-step iterations in convex metric space along with the directed graph. We demonstrate the Δ-convergence as well as the strong convergence results for these mappings. For supporting our main results we presented a numerical example and convergence comparison of modified Thianwan iteration with SP iteration scheme and Noor iteration scheme.

AB - In this article, we study the convergence behavior of G-nonexpansive mappings for three-step iterations in convex metric space along with the directed graph. We demonstrate the Δ-convergence as well as the strong convergence results for these mappings. For supporting our main results we presented a numerical example and convergence comparison of modified Thianwan iteration with SP iteration scheme and Noor iteration scheme.

KW - Convex metric spaces

KW - Directed graph

KW - Δ-convergence as well as strong convergence

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U2 - 10.1016/j.aej.2024.05.067

DO - 10.1016/j.aej.2024.05.067

M3 - Article

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SN - 1110-0168

VL - 102

SP - 1

EP - 9

JO - Alexandria Engineering Journal

JF - Alexandria Engineering Journal

ER -

Approximation theorems for G-nonexpansive mappings in convex metric spaces by three step iterations

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Keywords

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