New fixed point iteration and its rate of convergence

In the present paper, we introduce a new three-step fixed point iteration called SNIA-iteration (Naveen et al. iteration) which converges faster than the original iteration. It is possible by introducing a contraction operator on the existing iteration algorithm where the coefficients of the new ite...

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Bibliographic Details
Published in:Optimization 2023-09, Vol.72 (9), p.2415-2432
Main Authors: Chauhan (Gonder), Surjeet Singh, Kumar, Naveen, Imdad, Mohammad, Asim, Mohammad
Format: Article
Language:English
Subjects:
Contractive mapping
Convergence
convex metric space
convexity structure
fixed point
Iterative algorithms
rate of convergence
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Summary:In the present paper, we introduce a new three-step fixed point iteration called SNIA-iteration (Naveen et al. iteration) which converges faster than the original iteration. It is possible by introducing a contraction operator on the existing iteration algorithm where the coefficients of the new iterative process are chosen in instead of [0, 1]. The strong convergence result for the SNIA-iteration method is also proved by showing the convergence of this iteration method towards its fixed point. Further, the coefficients involved in SNIA-iteration have been interchanged, and then the result is compared with the original iteration. It is found that the new result is better than the previous one in the sense of its rate of convergence for contraction mappings.
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2022.2060830