Some New Convergence Approaches in Banach Spaces Involving the HK-Iteration Method with Application

Authors

Hanif Ullah Department of Mathematics, University of Lakki Marwat, Lakki Marwat 28440, KPK, Pakistan
Kifayat Ullah Department of Mathematics, University of Lakki Marwat, Lakki Marwat 28440, KPK, Pakistan
Ali Asghar Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Sindh, Pakistan
Muhammad Tariq Mathematics Research Center, Near East University, Near East Boulevard, PC: 99138, Nicosia/Mersin 10, Turkey https://orcid.org/0000-0001-8372-2532
Hijaz Ahmad Operational Research Center in Healthcare, Near East University, Nicosia/TRNC, 99138 Mersin 10, Turkey https://orcid.org/0000-0002-5438-5407
Mohamed F. Abouelenein Department of Insurance and Risk Management, College of Business, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia

DOI:

https://doi.org/10.37256/cm.6620258533

Keywords:

fixed point, HK-iteration, Banach space, condition (I), condition (E), differential equation

Abstract

The Banach spaces is the most popular and well-known spaces in the subject of pure mathematics. Many mathematicians have worked on different concepts from different angles in the field of functional analysis due to wide range of utilizations in quantum mechanics, optimization, and numerical analysis. In this paper, we explore the new iterative approach, namely HK-iteration method in Banach spaces. In addition, we investigate the some new convergence results in Banach Spaces via newly introduced concept with an application to a first-order delay differential equation. For the paper quality and reader's interest, numerical example and performance comparison via newly introduced concept have been added.

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Published

2025-11-27

Issue

Contemporary Mathematics, Volume 7 Issue 1 (2026), Forthcoming...

Section

Research Article

License

This work is licensed under a Creative Commons Attribution 4.0 International License.