A new fixed point algorithm for finding the solution of a delay differential equation

Chanchal Garodia; Izhar Uddin; Chanchal Garodia; Izhar Uddin

doi:10.3934/math.2020205

AIMS Mathematics

2020, Volume 5, Issue 4: 3182-3200. doi: 10.3934/math.2020205

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Research article

A new fixed point algorithm for finding the solution of a delay differential equation

Chanchal Garodia ,
Izhar Uddin ^,

Department of Mathematics, Jamia Millia Islamia, New Delhi-110025, India

Received: 10 November 2019 Accepted: 10 March 2020 Published: 26 March 2020
MSC : 47H09, 47H10, 54H25

In this paper, we construct a new iterative algorithm and show that the newly introduced iterative algorithm converges faster than a number of existing iterative algorithms. We present a numerical example followed by graphs to validate our claim. We prove strong and weak convergence results for approximating fixed points of Suzuki generalized nonexpansive mappings. Again we reconfirm our results by example and table. Further, we utilize our proposed algorithm to solve delay differential equation.
- Suzuki generalized nonexpansive mappings,
- fixed point,
- contractive-like mappings,
- iteration process,
- strong and weak convergence,
- delay differential equation
Citation: Chanchal Garodia, Izhar Uddin. A new fixed point algorithm for finding the solution of a delay differential equation[J]. AIMS Mathematics, 2020, 5(4): 3182-3200. doi: 10.3934/math.2020205

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Abstract

In this paper, we construct a new iterative algorithm and show that the newly introduced iterative algorithm converges faster than a number of existing iterative algorithms. We present a numerical example followed by graphs to validate our claim. We prove strong and weak convergence results for approximating fixed points of Suzuki generalized nonexpansive mappings. Again we reconfirm our results by example and table. Further, we utilize our proposed algorithm to solve delay differential equation.

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