Titlebook: Elementary Fixed Point Theorems; P.V. Subrahmanyam Textbook 2018 Springer Nature Singapore Pte Ltd. 2018 Partial order.Fixed Points.quasi-

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,Brouwer’s Fixed-Point Theorem, [.]). However, we provide here only the analytic proof of Brouwer’s theorem and a proof based on Sperner’s lemma. Needless to state that Brouwer’s theorem and its generalizations/variants find a wide range of applications in the solution of nonlinear equations, differential and integral equations, mathematical biology and mathematical economics.

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Basic Analytic Degree Theory of a Mapping, of view proposed by Heinz [.]. For more elaborate treatment, Cronin [.], Deimling [.], Lloyd [.] Outerelo and Ruiz [.] and Rothe [.] may be referred. It should be mentioned that Ortega and Rheinboldt [.] had provided a more accessible version of Heinz’s treatment.

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Contraction Principle,e applications of the contraction principle would fill volumes and Bollabos [.] 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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