Sehgal Type Contractions on Dislocated Spaces

Round 1

Reviewer 1 Report

The paper is devoted to studying an existence of fixed points of contractive type mappings acting on dislocated spaces.

I have the following remarks:

The authors should mention some applications of alpha -admissible mappings, if does exist.

After the equality (4.8)  the dash should be replaces by comma.

The results are new and I did not notice any errors.

Comments for author File: Comments.doc

Author Response

Dear Reviewer,

Thank you so much for your careful reading and comments.

We revised the lines "After the equality (4.8) "

Thank you for this remark.

The idea of alpha admissible is belong to mergeing 3 trends in fixed point theory:

1) results in standard metric space

2) results in a metric space endowed with a partial metric

3) results in the framework of CYCLIC mapping 

There is also some interesting result as a usage of alpha admissible mapping:

Bessem Samet

Fixed points for alpha-psi contractive mappings with an application to quadratic integral equations

Electron. J. Diff. Equ., Vol. 2014 (2014), No. 152, pp. 1-18.

Thanks for all.

Erdal KARAPINAR

Corresponding author.

Reviewer 2 Report

The paper is conceived in the environment of complete dislocated metric spaces, where fixed point theorems of type Sehgal are established under suitable control functions. The main result is obtained for selfmaps satisfying a general contractive condition, and this makes such theorem as general approach to several contexts. Indeed two point boundary value problems for a second order differential equation are shown as applications of the above theorem and its corollaries. This shows the real strength of the results here given as well.

Author Response

Dear Reviewer,

Thank you for your careful reading adn recommendation.

We have appreciated so much.

Thank you

Erdal Karapinar

Corresponding Author.