Ph.D. Tezi Görüntüleme

      In this thesis, it is aimed to find the existence and uniqueness of the common fixed point of various contraction mappings defined in modular 𝑏 −metric spaces and modular 𝑏 −metric spaces endow with Branciari distance function. In addition, the applicability of the obtained results to various fields of mathematics such as graph theory, homotopy, integral equations is also shown. Basically, this study consists of two main parts. In the first chapter, the development of fixed point theory, the concept of metric space and its properties, some basic definitions and theorems, the concept of fixed point, extensions of Banach fixed point theorem, graph theory and some generalized metric space structures are mentioned. In the second part, by using various auxiliary functions, the new concepts such as Suzuki Σ −contraction, 𝒢(Φ, ϑ, Ξ) −contraction, generalized 𝐹 −contraction involving quadratics terms, generalized Suzuki-Berinde 𝑍̂Θ −contraction and generalizedsimulation Θ̂℮ 𝛽 −contraction mappings are introduced. The common fixed point theorems obtained

      mathematical applications. Also, the modular 𝑏 −metric space equipped with the Branciari distance

      theorem on this space has been proved.