On a solution of a Delay Differential Equation, via a New Iteration Scheme

Manoj Kumar; Hemant Kumar Pathak

doi:https://doi.org/10.14445/22315373/IJMTT-V69I2P516

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 69 | Issue 2 | Year 2023 | Article Id. IJMTT-V69I2P516 | DOI : https://doi.org/10.14445/22315373/IJMTT-V69I2P516

On a solution of a Delay Differential Equation, via a New Iteration Scheme

Manoj Kumar, Hemant Kumar Pathak

Received	Revised	Accepted	Published
09 Jan 2023	11 Feb 2023	21 Feb 2023	28 Feb 2023

Citation :

Manoj Kumar, Hemant Kumar Pathak, "On a solution of a Delay Differential Equation, via a New Iteration Scheme," International Journal of Mathematics Trends and Technology (IJMTT), vol. 69, no. 2, pp. 124-146, 2023. Crossref, https://doi.org/10.14445/22315373/IJMTT-V69I2P516

Abstract

In this paper, results on stability and data dependency for a new iteration scheme under contractive- like mappings are discussed. In the framework of uniformly convex Banach spaces, we also provide weak and strong convergence results for mappings satisfying the condition βγ,μ. To validate our proofs, numerical example are also provided which are supported by graphs and tables. Finally, we exhibit the applicability of our three-step iteration process in delay differential equations.

Keywords

Contractive-like mappings, Bγ,μ condition, stability, data dependence, fixed points, iterative algorithm, weak and strong convergence, delay differential equation.

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