English abstract
Fixed point theory itself is a beautiful mixture of analysis (pure and applied), topology and geometry. Since Banach fixed point theorem (also called Banach contraction principle) in metric spaces appeared in 1922, there have been overwhelming trends in mathematical activities by using this theorem. This theorem presents numerous applications. It gives sufficient conditions under which equations have solutions. Some of these applications introduced in this study are Fredholm integral equation theorem and Volterra integral equation theorem. Over the last several decades, Kannan, Reich, Hardy-Rogers and other scholars have generalized this theorem greatly in several directions. One of the most influential generalization is from metric spaces to a more wide space called bmetric space. b-Metric spaces (also called metric type spaces) were introduced in 1998 by Czerwick [8]. Afterwards, a large number of fixed point theorems have been presented in such spaces. In this project, we have presented the notion of b-metric spaces, complete bmetric spaces, asymptotically regular sequences and maps in b-metric spaces, complex valued b-metric spaces and complex valued rectangular b-metric spaces. We provided some definitions, examples, fixed point theorems and finally an application to a linear equation.
