Revised and enhanced analysis of a recent novel iterative algorithm

Volume 18, Issue 2, pp 122--134 https://dx.doi.org/10.22436/jnsa.018.02.05

Publication Date: March 12, 2025 Submission Date: January 01, 2025 Revision Date: January 25, 2025 Accteptance Date: February 02, 2025

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Authors

K. Kumar - Department of Mathematics, Baba Mastnath University, Asthal Bohar-124021, Rohtak, Haryana, India. N. Hussain - Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia. V. Kumar - Department of Mathematics, KLP College, Rewari-123401, Haryana, India. S. Narwal - Department of Mathematics, Sat Jinda Kalyana College, Kalanaur-124113, Rohtak, Haryana, India.

Abstract

In this study, we rectify the recent results related to the stability of a novel iterative algorithm proposed by [P. Sharma, H. Ramos, R. Behl, V. Kanwar, J. Comput. Appl. Math., \( \bf 430\) (2023), 15 pages] using a broader concept of stability, known as weak \(w^2\)-stability. Additionally, to prove the resilience of this iteration, we establish new results regarding data dependency and weak convergence. We provide non-trivial examples to highlight the accuracy of our theoretical findings. Moreover, we demonstrated that the aforementioned iterative algorithm serves as a potential technique for solving a specific delay differential equation.

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Keywords

• Weak convergence
• weak \(w^2\)-stability
• data dependency
• equivalent sequence

MSC

•  47H09
•  47H10

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