Fixed Point Theorems in Metric Space and its Variants Using Various Contraction Conditions

Abstract

Fixed point theory with all its applications has become a very popular tool for solving problems in newlinemany branches of mathematical analysis and applied science. Various contraction conditions are newlineused in recent years to seek the existence of fixed point in metric space and its variants. Recently, newlinemany of the standard ideas of metric space have been extended to variants called b-Metric space, newlineParametric Metric Space, Parametric b-Metric Space, Non-Archimedean Menger Probabilistic newlineMetric Space etc. In order to find the fixed points of a certain mapping or the common fixed points newlineof pairs of mappings, researchers tried to generalize various contraction conditions, auxiliary newlinemappings, and metric spaces. In the present research work, we generalize and extends various newlinefixed point theorems in different metric spaces. The study is motivated from the research done by newlineleading researchers and their subsequent contributions in the real-world applications. The present newlinethesis consists of seven chapters in all. newline Chapter 1 describes the fundamental information in which some basic knowledge about newlinethe concepts of fixed point theory, Metric space and its variants and various contraction conditions. newlineThe description of the subsequent chapters of this thesis is also given in this chapter. newline In Chapter 2, A survey is given in the area of fixed point theory in which research is carried newlineout in Metric Space by various authors and it is presented here in chronological order. In addition, newlinethe latest references are also cited along with their systematic development in the present study. newlineMoreover, an overview of the thesis is also carried out in this chapter. newline