On fixed points of Geraghty contraction mappings in b-metric spaces

In recent years metric spaces ara generalized in various aspects and existing studies are carried to these newly defined spaces. One of the most important of these spaces is the b-metric spaces defined by Bakhtin in 1989. On the other hand generalizations of Banach fixed point theorem which is of great importance in fixed point theory are remarkable studies. To this end Geraghty defined a new class of mapping in 1973 and proved the existence and uniqueness of the fixed point of this mapping defined in complete metric spaces. In this thesis, articles about the fixed points of the Geraghty and α-Geraghty, (α,β)-Geraghty, α-φ-Geraghty and (B) type α-φ-Geraghty mappings which are generalized Geraghty mappings in b-metric spaces are compiled. The applications of theorems to integral equations is discussed in the thesis and the results are discussed in the conclusion and recommendations section.