Soft fixed point theorems in Steinhaus transform soft metric spaces

In this thesis study, firstly definitions and theorems about soft set theory, soft topolojical spaces, soft metric spaces, fixed point theory and soft fixed point theory which are basic concepts fort the methods and techniques we used throughout the study are given. The Steinhaus transform soft metric which is symbolized by D_p is defined considering soft sets with a parameter set. By giving the definitions of concepts such as soft sequence, soft convergent sequence, soft Cauchy sequence, soft contraction mapping, soft fixed point in Steinhaus transform soft metric spaces, the necessary background has been created in order to obtain and prove the soft fixed point theorems for the thesis study. Banach contraction theorem has been proved for Steinhaus transform soft metric spaces as research findings. Then soft fixed point theorems have been obtained in Steinhaus transform soft metric spaces by using Kannan and Caristi type contractions. Finally, by defining the cyclic contraction mapping in Steinhaus transform soft metric spaces, a new Kannan type soft fixed point theorems is proved.