Fixed Point Theorems in Extended b metric Space and its Variants

Abstract

Theory of fixed point is a branch of mathematics that deals with the existence and properties of newlinefixed points of functions. A fixed point of a function is a point that is mapped to itself under the newlinefunction. In metric spaces, fixed point theory is concerned with the study of functions that have at newlineleast one fixed point. In fixed point theory the concept of a contraction mapping is used widely. A newlinecontraction mapping is a function that reduces the distance between two points in a metric space. newlineThe significance of the contraction property is that it guarantees the existence and uniqueness of newlinea fixed point. newlineThe present study is motivated from the research done by leading researchers and their subsequent newlinecontributions in the real-world applications. This thesis consists of eight chapters in all. newline Chapter 1 describes the fundamental information in which some basic knowledge about newlinethe concepts of fixed point theory, contraction conditions and metric space with its variants are newlinediscussed. The description of the subsequent chapters of this thesis is also given in this chapter. newline Chapter 2, a literature survey is done in which research is carried out in the area of fixed newlinepoint theory in different metric spaces by various authors which is presented here in chronological newlineorder. In addition, this chapter gives the systematic progress of f newline