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Degree Theory, k-Set Contractions and Condensing Operators

In: An Introduction to Nonlinear Analysis and Fixed Point Theory

Author

Listed:
  • Hemant Kumar Pathak

    (Pandit Ravishankar Shukla University, School of Studies in Mathematics)

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.

Suggested Citation

  • Hemant Kumar Pathak, 2018. "Degree Theory, k-Set Contractions and Condensing Operators," Springer Books, in: An Introduction to Nonlinear Analysis and Fixed Point Theory, chapter 0, pages 449-511, Springer.
    • Handle: RePEc:spr:sprchp:978-981-10-8866-7_6
    DOI: 10.1007/978-981-10-8866-7_6
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