On Various Fixed Point Theorems and Applications in Different Type Metric Spaces
Project no. 22080 · Status: Kapanmış · 2020
Summary
In this project, some basic definitions and concepts related to metric fixed point theory are first introduced. The first result of the project is to define the notion of a modular $p$-metric space (an extended modular $b$-metric space) and some fixed point results are proved for $\alpha$-$\widehat{\nu}$-Meir-Keeler contractions in this new space. Using these results, some new fixed point theorems are deduced in extended modular metric spaces endowed with a graph and in partially ordered extended modular metric spaces. Then, an important relation between fuzzy-Meir-Keeler and extended fuzzy $p$-metric is given and certain new fixed point results are obtained in triangular fuzzy $p$-metric spaces. An example and an application are provided to support results which generalize several well known results in the literature. As another important outcome of the project, the generalized $(\psi,\alpha,\beta)$-weak contraction is introduced and some fixed point theorems in the frame work of $b$-metric space are proved. Further, some examples and an application are provided to support theorems. In the last part of the project, it is stated that the objectives of the project are successfully achieved, a significant contribution is made to the literature and some clear problems are included for those who do research on this subject.