A Tseng-Type Algorithm with Self-Adaptive Techniques for Solving the Split Problem of Fixed Points and Pseudomonotone Variational Inequalities in Hilbert Spaces
Round 1
Reviewer 1 Report
This paper contains abstract, introduction (the motivation for research), preliminaries (4 known lemmas), main results (1 new theorem, 1 new remark, 2 new algorithms, 1 new corollary) and references (48 items).
Upon reviewing the paper I have made the following remarks:
- in whole paper it should write
- "+∞" instead of "∞";
- "limk→+∞" instead of "limk→∞";
- "for all" instead of "∀";
- "there exists" instead of "∃";
- "implies" instead of "⇒";
- "if and only if" instead of "⇔".
General opinion
This paper contains several new and original results. All the proofs seem to be correct. The paper contains an adequate algorithm instead of application. The overall paper is well-written. Therefore, I recommend that the paper be revised according to the cited remarks. Re-revision is necessary.
Author Response
Response: We have revised the paper point-by-point according to your
suggestions. Thank you very much for your help!
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments are given in the file.
Comments for author File: Comments.pdf
Author Response
Response: We have revised the paper point-by-point according to your
suggestions. Thank you very much for your help!
Author Response File: Author Response.pdf
Reviewer 3 Report
The paper is well written. Authors improved technique and present Tseng-type iterative algorithm for solving the split problem by using self-adaptive techniques.
For the ease of monitoring I suggest to include relationship between $<f,g>$ and $\parallel{f-g\parallel}$ as well as basic properties used in paper.
Through whole paper check typos.
It will be nice include some applications.
Comments for author File: Comments.pdf
Author Response
Response: We have revised the paper point-by-point according to your
suggestions. Thank you very much for your help!
Author Response File: Author Response.pdf
Reviewer 4 Report
See attached file.
Comments for author File: Comments.pdf
Author Response
Response: We have added an application
and a concluding remark.
Response: In this
paper, we construct Algorithm 1 which only has weak convergence.
Response: We have cited the above four references in our paper, see
references [49,50,51,52].
Response: We have revised the paper point-by-point according to your
suggestions. Thank you very much for your help!
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
Authors made corrections according to reviewers comments. Please, check inequality (1) once more, seems that it is still incomplete.
Reviewer 4 Report
The paper has been improved. It contains original results and it is well-formalized and well- written.
