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Mathematics
Volume 10
Issue 20
10.3390/math10203720
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Article
Peer-Review Record

Some New Results on Convergence, Weak w2-Stability and Data Dependence of Two Multivalued Almost Contractive Mappings in Hyperbolic Spaces

Mathematics 2022, 10(20), 3720; https://doi.org/10.3390/math10203720
by Austine Efut Ofem 1,*, Jacob Ashiwere Abuchu 1,2, Reny George 3,*, Godwin Chidi Ugwunnadi 4,5 and Ojen Kumar Narain 1
Reviewer 1: Anonymous
Reviewer 2:
Manuel De La Sen
Mathematics 2022, 10(20), 3720; https://doi.org/10.3390/math10203720
Submission received: 14 September 2022 / Revised: 4 October 2022 / Accepted: 6 October 2022 / Published: 11 October 2022
(This article belongs to the Special Issue Advances in Fixed Point Theory and Its Applications)

Round 1

Reviewer 1 Report

This paper constitutes a fine contribution to (set-valued) fixed point theory in the important class of hyperbolic spaces. Its main results can be found in Sections 2--5. Section 6 contains illuminating numerical examples. My recommendation is that (a revised version of) the paper be accepted for publication in "Mathematics". When the authors prepare the revised version of their paper, they should take into account the following comments and suggestions.

(1) Title (and elsewhere): "almost contraction mappings" ---> "almost contractive mappings"

(2) Line 2: please see the first item above.

(3) Line 3: "concepts" ---> "concepts of"

(4) Line 5: "of new" ---> "of our new"

(5) Line 11: "setting" ---> "setting of"

(6) Line 64: "known known" ---> "known"

(7) Line 97: "fill" ---> "to fill"

(8) Examples 1 and 2: could also higher-dimensional examples be provided?

(9) Line 368: what is the meaning of the question mark?

(10) Line 370: please see item (9) above.

Author Response

Find attached a pdf file containing the responses to the reviewer's comments.

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper is well-worked and well-formalized and it contains new results of interest for the readers of this journal. Some minor points to clarify to facilitate the readability follow below:

Proof of Theorem 3, Penultimate inequaliity: How is the L-constant absorbed to obviate the second summand in the upper-bound of (1) if L>0?.

Line 2 before Example 1: "neither contractive nor expansive mappings".

Same concern for  details in the parallerl proof of Theorems 4, 5.

Proof of Theorem 4: It is not mentioned how is d(s/k, q*) addressed in (21) to get  the limit d(x/k. q*) equal to zero. Supposedly d(s/k, q*) is supposed or proved to have a zero limit as k tends to infinity but the concrete used details are not mentioned.

In the conclusions , ref. 29 appears with a question mark.

Author Response

Find attached a pdf file containing the responses to the reviewer's comments.

Author Response File: Author Response.pdf

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