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Topics in Fixed Point Theory pp 33–64Cite as

Banach Contraction Principle and Its Generalizations

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Abstract

In 1922, the Polish mathematician Stefan Banach established a remarkable fixed point theorem known as the “Banach Contraction Principle” (BCP) which is one of the most important results of analysis and considered as the main source of metric fixed point theory. It is the most widely applied fixed point result in many branches of mathematics because it requires the structure of complete metric space with contractive condition on the map which is easy to test in this setting. The BCP has been generalized in many different directions. In fact, there is vast amount of literature dealing with extensions/generalizations of this remarkable theorem. In this chapter, it is impossible to cover all the known extensions / generalizations of the BCP. However, an attempt is made to present some extensions of the BCP in which the conclusion is obtained under mild modified conditions and which play important role in the development of metric fixed point theory.

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  1. Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Abdul Latif

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  1. Abdul Latif
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  1. Department of Mathematics, University of Tabuk, Tabuk, Saudi Arabia

    Saleh Almezel

  2. Department of Mathematics, Aligarh Muslim University, Aligarh, Uttar Pradesh, India

    Qamrul Hasan Ansari

  3. Department of Mathematical Sciences, University of Texas at El Paso, El Paso, Texas, USA

    Mohamed Amine Khamsi

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Latif, A. (2014). Banach Contraction Principle and Its Generalizations. In: Almezel, S., Ansari, Q., Khamsi, M. (eds) Topics in Fixed Point Theory. Springer, Cham. https://doi.org/10.1007/978-3-319-01586-6_2

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