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

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 Hanif-Kifayat (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.