Study Of Fixed Point Theorems In Fuzzy Metric Space And Its Application

Abstract

The research report in this thesis deals mainly with fixed point theorems of fuzzy newlinemetric space and their applications. We have proved that for three continuous self newlinemappings of fuzzy metric space, there exists a unique common fixed point. We have newlineestablished that when the condition of occasionally weakly compatible mapping is newlinesatisfied by three pairs of continuous self mappings, a common fixed point for the newlinesame exists. Next, we discuss the R-weakly commuting mapping and show that for newlinethree continuous self mappings, satisfying the condition of R-weakly commuting have newlinea unique common fixed point. Further, we extend our result for the three pairs of newlinecontinuous self mapping, satisfying the property (E.A.) and implicit relation by newlineshowing the existence of unique common fixed point. newlineFinally, the existence of unique common fixed point for three pairs of occasionally newlineweakly compatible mapping is established under the constraint of the integral type newlineinequality in fuzzy metric space.. newlineBesides, the application of fuzzy logic models in various fields is discussed. First we newlinedeveloped a fuzzy logic model to forecast momentum in stock market. Then we also newlinedevelop forecasting model based on stock market sensex using fuzzy logic. newline