Degree Theory, k-Set Contractions and Condensing Operators

Hemant Kumar Pathak ()
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Hemant Kumar Pathak: Pandit Ravishankar Shukla University, School of Studies in Mathematics

Chapter Chapter 6 in An Introduction to Nonlinear Analysis and Fixed Point Theory, 2018, pp 449-511 from Springer

Abstract: Abstract The notion of “degree” of a map was first defined by Brouwer, who showed that the degree is homotopy invariant, and used it to prove the Brouwer fixed point theorem. Note that topological degree theory is a generalization of the winding number of a curve in the complex plane. It is closely connected to fixed point theory and can be used to estimate the number of solutions of an equation. For a given equation, if one solution of an equation is easily found, then degree theory can often be used to prove existence of a second, nontrivial, solution.

Date: 2018
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DOI: 10.1007/978-981-10-8866-7_6

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