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Fixed point theorems are broadly studied for three classes of mappings namely continuous, contractive and non-expansive mappings. Best approximation and best proximity theorems are studied as an extension of fixed point theorems. So far, both these extensions have been studied only for continuous mappings and in some restricted spaces for non- expansive mappings. This book gives extension results for fixed point theorems of contractive mappings. There are quite a number of problems in integral and differential equations, for which solutions can be equivalently formulated as a fixed point of some operator, on a suitable space. So fixed point theorems serve as a powerful tool for tackling these type of problems. It has also found diverse applications in areas like game theory and mathematical Economics.