A New Advanced Class of Convex Functions with Related Results
Round 1
Reviewer 1 Report
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Author Response
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Reviewer 2 Report
In this under review paper, the authors first introduced a new class of convex functions which is called "coordinate strongly (\eta_1, \eta_2)-convex functions". The results are correct and the paper is well written. I recommend the paper for publication in Axioms after the following corrections.
1) I recommend the authors to use "coordinated strongly (\eta_1, \eta_2)-convex functions" or "strongly (\eta_1, \eta_2)-convex functions on coordinates " instead of "coordinate strongly (\eta_1, \eta_2)-convex functions". Then it should be changed in the whole paper.
2) Page 6, Line 10 :It should be a dot at the end of equation. THen it should be started the next sentences as "This gives..."
3) The authors use H-H inequality for strongly \eta-convex functions in the first step of the proof of Theorem 2.6. The authors should give this inequality in the introduction section.
Author Response
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Reviewer 3 Report
In this paper, the authors propose an advanced class of convex functions associated with strong $\eta$-convexity and also investigate some interesting related properties. The results presented are apparently new with the corresponding references to the previously known facts. To my mind, the paper is acceptable for publication.
Author Response
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Reviewer 4 Report
An article about a new class of convex functions that is positively surprising.
The introduction contains enough references for the reader to be able to understand the methodological aspects, under which the article was built, in order to be able to intuit the impact of the contents exposed in the respective area.
It is certainly not an easy-to-read article, but it has the necessary strength to become a good reference in this field of investigation.
However, the examples were not the best, nor was their resolution simplified in order to extract the best that the scientific component, which is well explained, could offer. I suggest that you simplify the resolution of the examples, as well as better explain the transition to the last lines, which is not clear.
The proof of theorem 3.4. seems to contain an error, because something doesn't add up, but that should be easy for the authors to resolve.
Author Response
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Author Response File: Author Response.pdf
