A General Theorem on the Stability of a Class of Functional Equations Including Quartic-Cubic-Quadratic-Additive Equations
Round 1
Reviewer 1 Report
see attachement
Comments for author File: 
Comments.pdf
Author Response
The first reviewer suggests to add some papers into the list of References and I included four papers written by Brzdek et al. and Popa et al. and by Qarawani in the list of References and they were all cited in Introduction. Basides I did not include papaers written by Jung et al. because these papers are weakly connected to the present paper (see Introduction and References of the revised manuscript).
Two papers published most recently in the Mathematics were included in References and they were discussed in comparison with the present paper in the last part of Introduction.
As the reviewer suggested, I explained more precisely by inserting many steps /lines more in the proof of Theorem 3.1. I wish that this improvement helps the reader for easier understaning.
I introduced 5 main theorems in this paper. Each theorem can be applied under the special conditions different from the conditions for other main theorems. Therefore, all of five main theorems are equally important.
Reviewer 2 Report
The authors consider n-dimensional quartic-cubic-quadratic-additive type functional equations of the form
\[
\sum_{i=1}^{l}c_if(a_{i1}x_1+...+a_{in}x_n)= 0.
\]
The author prove some general stability theorems of a large class of functional equations which includes quartic-cubic-quadratic-additive functional equations using direct method.
The paper is documented and organized, starting with an introduction in the subject. The concepts and purpose are clearly explained, the proofs are accurate, the references cited include some of the major results in the area.
Author Response
The authors of this paper are very much thankful to this anonymous reviewer for his/her careful reading and very positive comments. This reviewer encourages us much. Thank you again.
Round 2
Reviewer 1 Report
Accept in present form
