Fixed Point Theory is a striking mixture of analysis as well as Topology. There are plenty of problems in applied mathematics which can be solved by means this theory. Still, practice proves that in many real situations an approximate solution is more than sufficient, so the existence of fixed points is not strictly required. We have establish some fixed point results in cone metric space and approximate fixed point results in metric spaces under various contraction conditions.

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Dr. Shweta Sachdeva and Dr. Pankaj Kumar Mishra, M.Phil.(Mathematics), Ph.D.(Mathematics), Assistant Professor, Department of Mathematics, University of Petroleum and Energy Studies, Dehradun, India.