Growing specialization and diversification have brought a host of monographs and theses on increasingly specialized topics. However, the tree of knowledge of mathematics and related field does not grow only by putting forth new branches. It also happens quite often in fact that branches which were thought to be completely disparate are suddenly seen to be related.It is apparent that the fixed point theory has now reached a level of maturity appropriate to an examination of its central themes. The topics selected for this thesis were chosen accordingly. No attempt has been made to explore all aspects of the theory nor to present a compendium of known facts. Our objective is merely to offer the mathematical community an accessible self contained document which can be used as an introduction to the subject and its development. We have attempted to render the major results understandable to wide researches, including non specialists and at the same time to provide a source for examples references and new approaches for currently working in the topic.

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