A FIXED POINT PROBLEM VIA SIMULATION FUNCTIONS IN INCOMPLETE METRIC SPACES WITH ITS APPLICATION

Özet

In this 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 inincomplete metric spaces. Secondly, as motivated by the recent work of A.H. Ansari etal. [J. Fixed Point Theory Appl. (2017), 1145–1163], we obtain that an existence anduniqueness result for the following problem: findingx∈Xsuch thatx=Tx,AxR1BxandCxR2Dx, where (X,d) is an incomplete metric space equipped with the two binaryrelations R1and R2,A,B,C,D:X→Xare discontinuous mappings andT:X→Xsatisfies in a new contractive condition. This result is a real generalization of maintheorem of A.H. Ansari’s. Finally, we provide some examples for our results and as anapplication, we find that the solutions of a differential equation.