Novel Noor iterations technique for solving nonlinear equations

Chonjaroen Chairatsiripong; Tanakit Thianwan; Chonjaroen Chairatsiripong; Tanakit Thianwan

doi:10.3934/math.2022612

AIMS Mathematics

2022, Volume 7, Issue 6: 10958-10976. doi: 10.3934/math.2022612

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Research article

Novel Noor iterations technique for solving nonlinear equations

Department of Mathematics, School of Science, University of Phayao, Phayao, 56000, Thailand

Received: 24 December 2021 Revised: 12 March 2022 Accepted: 27 March 2022 Published: 06 April 2022
MSC : 47H09, 47H10

The aim of this paper is to propose a novel Noor iteration technique, called the CT-iteration for approximating a fixed point of continuous functions on closed interval. Then, a necessary and sufficient condition for the convergence of the CT-iteration of continuous functions on closed interval is established. We also compare the rate of convergence between the proposed iteration and some other iteration processes in the literature. Specifically, our main result shows that CT-iteration converges faster than CP-iteration to the fixed point. We finally give numerical examples to compare the result with Mann, Ishikawa, Noor, SP and CP iterations. Our findings improve corresponding results in the contemporary literature.
- convergence theorem,
- convergence rate,
- continuous function,
- fixed point,
- closed interval
Citation: Chonjaroen Chairatsiripong, Tanakit Thianwan. Novel Noor iterations technique for solving nonlinear equations[J]. AIMS Mathematics, 2022, 7(6): 10958-10976. doi: 10.3934/math.2022612

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Abstract

The aim of this paper is to propose a novel Noor iteration technique, called the CT-iteration for approximating a fixed point of continuous functions on closed interval. Then, a necessary and sufficient condition for the convergence of the CT-iteration of continuous functions on closed interval is established. We also compare the rate of convergence between the proposed iteration and some other iteration processes in the literature. Specifically, our main result shows that CT-iteration converges faster than CP-iteration to the fixed point. We finally give numerical examples to compare the result with Mann, Ishikawa, Noor, SP and CP iterations. Our findings improve corresponding results in the contemporary literature.

References

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