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The problems associated in the present research work which are taken care of are related to the study of fixed point theorems in semi Hausdorff space, uniform space and Banach space along with studying the applications of fixed point theorem in economics and analyzing the theory of fractals and application of fixed point theory. In this work, the introductory part of fractal theory, the important applications of fractal in image compression and a model of fixed point theorem in dynamical system is taken into consideration keeping in view its application in various areas like planetary motion,...