Schauder’s Fixed Point Theorem and Allied Theorems

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


Attempts to extend Brouwer’s fixed point theorem to infinite dimensional spaces culminated in Schauder’s fixed point theorem [20]. The need for such an extension arose because existence of solutions to nonlinear equations, especially nonlinear integral and differential equations can be formulated as fixed point problems in function-spaces. This chapter discusses Schauder’s and allied fixed point theorems with their applications including the existence of Haar integral, invariant mean and Banach limit.


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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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