Abstract
Metric fixed point theory refers to the fixed point theoretical results in which geometric conditions on the underlying spaces and or mappings play a crucial role. The first ever fixed point theorem in metric space appeared in explicit form in Banach's thesis, known as the Banach Contraction Principle (BCP), used to establish the existence of a solution to an integral equation. Due to its simplicity and elegant proof, it is perhaps the most widely applied fixed point theorem in many branches of mathematics. The BCP has been generalized in different directions. In the chapter presents some well known extensions and generalizations of BCP which play an important role in the development of metric fixed point theory.
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