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Peer-Review Record

On the Semi-Local Convergence of a Jarratt-Type Family Schemes for Solving Equations

Foundations 2022, 2(1), 234-241; https://doi.org/10.3390/foundations2010017
by Christopher I. Argyros 1, Ioannis K. Argyros 2,*, Stepan Shakhno 3 and Halyna Yarmola 4
Reviewer 2: Anonymous
Foundations 2022, 2(1), 234-241; https://doi.org/10.3390/foundations2010017
Submission received: 24 January 2022 / Revised: 10 February 2022 / Accepted: 15 February 2022 / Published: 17 February 2022
(This article belongs to the Special Issue Iterative Methods with Applications in Mathematical Sciences)

Round 1

Reviewer 1 Report

Authors studied semi-local convergence of two-step Jarratt-type method for solving nonlinear equations under the classical Lipschitz conditions for first-order derivatives. The results are very interesting. This paper can be accepted for publication.

Author Response

Dear Reviewer, 

First, we thank you for your valuable time and effort to make this manuscript a better paper. We have made all the changes as per your valuable feedback and recommendation. 

With Best Regards,
Prof Dr. Ioannis K. Argyros, 

Reviewer 2 Report

To the best of my knowledge, this algorithm can be considered also in the case when the first derivatives are H\"older continuous instead of the Lipschitz conditions. The result presented here can be generalized for such a class of problems?

Author Response

Dear Reviewer, 

First, we thank you for your valuable time and effort to make this manuscript a better paper. We have made all the changes as per your valuable feedback and recommendation. Please find the attached pdf for your one-to-one response to your comments. 

With Best Regards,
Prof Dr. Ioannis K. Argyros, 

Author Response File: Author Response.pdf

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