Approximating Fixed Points of Nonexpansive Type Mappings via General Picard–Mann Algorithm
Benoit Morel
Round 1
Reviewer 1 Report
This paper ought to be published, just because of the exhaustive review of the different algorithms developed in the context of approximating fixed points in problematic situations. Just that and their demonstration of convergence in the context of the “Picard-Mann” algorithm sheds a lot of light on the subject and will be helpful to potential readers who want to understand the problem.
Author Response
We are very much grateful to the reviewer for reviewing our manuscript titled 'Approximating fixed points of nonexpansive type mappings via general Picard-Mann algorithm" and recommending it for publication. We have done the spell check throughout the paper and corrected all the errors.
Reviewer 2 Report
In the paper under review the authors study approximate fixed points of nonexpansive type mappings in Banach spaces using a general Picard-Mann algorithm. The weak and strong convergence of iterates is proved. Numerical examples are provided. The results of the paper are new and interesting. The proofs seem to be correct and the paper is well-written. Therefore I recommend its acceptance subject to a minor revision. Below are my specific comments.
1. The definition of a nonexpansive mapping on page 1 should be displayed. 2. The notation $F(\phi)$ appears in Lemma 1.4. I think that this is the set of fixed points of the map $\phi$. But I did not find its definition. 3. Theorem 4.3 is proved under assumption that the set of fixed points $F(\phi)$ is not empty. This should be stated explicitly including the abstract.Author Response
We are very much grateful to the reviewer for reviewing our manuscript titled 'Approximating fixed points of nonexpansive type mappings via general Picard-Mann algorithm" and recommending it for publication. We have effected all the corrections pointed out by the reviewer. Please find the attached file.
Author Response File: 
Author Response.pdf
