A fixed point problem with constraint inequalities via a contraction in non-complete metric spaces
Abstract
In the present paper, firstly, we review the notion of the SO-complete metric spaces. This notion
let us to consider some fixed point theorems for single-valued mappings in non-complete metric spaces.
Secondly, as motivated by the recent work of H. Baghani et al.(A fixed point theorem for a new class of
set-valued mappings in R-complete (not necessarily complete) metric spaces, Filomat, in press), we obtain
the results of Ansari et al. [J. Fixed Point Theory Appl. (2016), doi:10.1007/s11784-016-0320-1] with very
much weaker conditions. Also, we provide some examples show that our main theorem is a generalization
of previous results. Finally, we give an application to the system of differential equations for our result.
let us to consider some fixed point theorems for single-valued mappings in non-complete metric spaces.
Secondly, as motivated by the recent work of H. Baghani et al.(A fixed point theorem for a new class of
set-valued mappings in R-complete (not necessarily complete) metric spaces, Filomat, in press), we obtain
the results of Ansari et al. [J. Fixed Point Theory Appl. (2016), doi:10.1007/s11784-016-0320-1] with very
much weaker conditions. Also, we provide some examples show that our main theorem is a generalization
of previous results. Finally, we give an application to the system of differential equations for our result.
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