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Abstract The theory of xed point is concerned with the conditions which guarantee that the operator T : X ! X of a topological space X onto itself admits one or more xed points, that is, point x 2 X for which x = T(x). This theory began in 1912 with the work of Brouwer, who proved that any continuous self-mapping of a closed unit ball of n-dimensional Euclidean space has at least one xed point. The other fundamental result of Brouwer;s xed point theorem was given by Banach in 1922 which is popularly known as a Banach Contraction Principle or contraction mapping theorem of Banach. |