Generalization of Mappings and Fixed Point Theorems in Metric Spaces and D Metric Spaces

Abstract

The study of metric spaces is important in the subject of Analysis and newlineTopology. The concept of metric space is very important for formulating the physical newlineand mathematical problems which arise in nonlinear Functional Analysis and newlineTopology. The Mathematician M. Frechet in 1906, firstly introduced the notion of newlinemetric space and further development of that notion is developed by Hausdroff in newline1914. The Metric space is fundamental in the study of topology and functional newlineanalysis .The study of metric space is one of the best and powerful tools for study of newlinefixed point theorems. Recently the metric spaces have gained importance due to the newlinedevelopment of the metric fixed point theory. newlineFixed point theory is an important and major topic of the nonlinear newlinefunctional analysis . The topic of finding the fixed point of the mapping has been the newlinemost active area of research work in subject of analysis and topology since long time. newlineFixed Point theory is beautiful mixture of Analysis (pure and applied ), Topology and newlineGeometry. Many problems in mathematical science and engineering have been solved newlineby fixed point theory of non expansive and non expansive type single and multivalued newlinemaps. Study of fixed points of self mappings satisfying contractive conditions newlineis one of the research activity. Large number of fixed point results have been proved newlinefor self-mappings satisfying various types of contractive conditions and inequalities. newlineTherefore it is interesting to study the fixed point theorems for various classes of newlinemappings in metric as well as D-Metric spaces. newlineStefan Banach ( 1892-1945 ) was the famous Polish Mathematician newlinewho was one of the founders of fixed point theory. In 1922 Banach proved important newlinefixed point results on contractive type mappings. Generalization of Banach fixed point newlinetheorem has been deeply investigated as branch of research, so far, according to newlineimportance and simplicity, many authors have obtained, interesting extensions and newlinegeneralization of the Banach contraction principle. newlineNumber of interesting results have