A novel scheme of $ k $-step iterations in digital metric spaces

Thongchai Botmart; Aasma Shaheen; Afshan Batool; Sina Etemad; Shahram Rezapour; Thongchai Botmart; Aasma Shaheen; Afshan Batool; Sina Etemad; Shahram Rezapour

doi:10.3934/math.2023042

AIMS Mathematics

2023, Volume 8, Issue 1: 873-886. doi: 10.3934/math.2023042

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Research article

A novel scheme of $ k $-step iterations in digital metric spaces

1.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
2.
Department of Mathematical Sciences, Fatima Jinnah Women University, Islamabad, Pakistan
3.
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
4.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

Received: 05 August 2022 Revised: 14 September 2022 Accepted: 19 September 2022 Published: 12 October 2022
MSC : 39B72, 46C05

In computational mathematics, the comparison of convergence rate in different iterative methods is an important concept from theoretical point of view. The importance of this comparison is relevant for researchers who want to discover which one of these iterations converges to the fixed point more rapidly. In this article, we study the different numerical methods to calculate fixed point in digital metric spaces, introduce a new k-step iterative process and conduct an analysis on the strong convergence, stability and data dependence of the mentioned scheme. Some illustrative examples are given to show that this iteration process converges faster.
- digital metric space,
- iterative method,
- fixed point schemes
Citation: Thongchai Botmart, Aasma Shaheen, Afshan Batool, Sina Etemad, Shahram Rezapour. A novel scheme of $ k $-step iterations in digital metric spaces[J]. AIMS Mathematics, 2023, 8(1): 873-886. doi: 10.3934/math.2023042

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Abstract

In computational mathematics, the comparison of convergence rate in different iterative methods is an important concept from theoretical point of view. The importance of this comparison is relevant for researchers who want to discover which one of these iterations converges to the fixed point more rapidly. In this article, we study the different numerical methods to calculate fixed point in digital metric spaces, introduce a new k-step iterative process and conduct an analysis on the strong convergence, stability and data dependence of the mentioned scheme. Some illustrative examples are given to show that this iteration process converges faster.

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