Some Novel Inequalities for LR-(k,h-m)-p Convex Interval Valued Functions by Means of Pseudo Order Relation
, Rajagopalan Ramaswamy 2,†, Ola A. Ashour Abdelnaby 2,† and Stojan Radenović 3Round 1
Reviewer 1 Report
The Jensen inequality which exploits the standard notion of convexity is a very useful tool, for example, in the theory of probability and related areas. That's why its generalizations may bring some new insights as well as some new findings in these areas. In the latest decades, the theory of fractional processes became much more developments, and the paper presents some very analytical versions of fractional inequalities which may be also useful.
Author Response
Answer to reviewer :
Comment: The Jensen inequality which exploits the standard notion of convexity is a very useful tool, for example, in the theory of probability and related areas. That’s why its generalizations may bring some new insights as well as some new findings in these areas. In the latest decades, the theory of fractional processes became much more developments, and the paper presents some very
analytical versions of fractional inequalities which may be also useful.
Response: Dear reviewer. We are ever so thankful for your opinion. Thank you so much for your nice words.
Waiting eagerly to hear from you a positive response in this regard.
With best regards.
Sincerely yours
Vuk Stojiljkovi´c
On behalf of the authors:
Vuk Stojiljkovi´c, Rajagopalan Ramaswamy , Ola A. Ashour Abdelnaby, Stojan Radenovi´c
Reviewer 2 Report
AUTHORS MUST STRENGTHEN THE INTRODUCTION PART
Author Response
Answer to reviewer :
Comment: AUTHORS MUST STRENGTHEN THE INTRODUCTION PART
Response: Dear reviewer. We are ever so thankful for your opinion. Thank you for your comment. We have improved the introduction part.
Waiting eagerly to hear from you a positive response in this regard.
With best regards.
Sincerely yours
Vuk Stojiljkovi´c
On behalf of the authors:
Vuk Stojiljkovi´c, Rajagopalan Ramaswamy , Ola A. Ashour Abdelnaby, Stojan Radenovi'c
Reviewer 3 Report
Please see attached file.
Comments for author File: 
Comments.pdf
Author Response
Please see the pdf file. Thank you.
All the best,
Author Response File: Author Response.pdf
Round 2
Reviewer 3 Report
1) In Definition 3, the authors introduce the Katugampola fractional integral operator for interval valued function and show the operators as the symbol J. However, in the paper the authors use the same symbol for Katugampola fractional integral operator for REAL valued function. They should be different symbols. I mean it should be shown the integrals of F_* and F^* by different symbol from J.
2) The first paper on fractional Hermite-Hadamard inequalities for IVF should be cited in this paper.
3) It should be "Katugampola " instead of "Katagumpola" at Page 8, Line 15.
Author Response
Answer to reviewer :
Comment: 1) In Definition 3, the authors introduce the Katugampola fractional integral operator for interval valued function and show the operators as the symbol J. However, in the paper
the authors use the same symbol for Katugampola fractional integral operator for REAL valued
function. They should be different symbols. I mean it should be shown the integrals of F∗ and F
∗
by different symbol from J.
2) The first paper on fractional Hermite-Hadamard inequalities for IVF should be cited in this
paper.
3) It should be ”Katugampola ” instead of ”Katagumpola” at Page 8, Line 15.
Response: Dear reviewer. We are ever so thankful for your opinion. We are listing what we
have changed.
1. We have changed the symbol from J to chi.
2. We have cited the first paper on fractional HH inequalities of IVF type.
3. We have changed the Katagumpola to Katugampola.
Waiting eagerly to hear from you a positive response in this regard.
With best regards.
Sincerely yours
Vuk Stojiljkovi´c
On behalf of the authors:
Vuk Stojiljkovi´c, Rajagopalan Ramaswamy , Ola A. Ashour Abdelnaby, Stojan Radenovi´c
Author Response File: Author Response.pdf
