Contraction Principle

  • P. V. SubrahmanyamEmail author
Part of the Forum for Interdisciplinary Mathematics book series (FFIM)


The contraction mapping principle proved independently by Banach [1] and Cacciopoli [7] is a fundamental fixed point theorem, with an elementary proof. This theorem has a wide spectrum of applications and is a natural choice in approximating solutions to nonlinear problems. According to Rall [18], the applications of the contraction principle would fill volumes and Bollabos [4] calls it a doyen of fixed point theorems. Charmed by both the simplicity and utility of this theorem, many authors have generalized it in diverse directions. This chapter samples a few of these.


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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology MadrasChennaiIndia

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