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Fixed Point Theorems

In: An Introduction to Nonlinear Analysis and Fixed Point Theory

Author

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  • Hemant Kumar Pathak

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

Abstract

In Sect. 5.1, we discuss the Banach’s contraction mapping theorem and some consequences of this theorem. We also deal with contractive mappings considered by Edelstein [212] and certain generalizations of contraction mapping theorem, mainly the ones obtained by Boyd and Wongs [75], Kannan [308, 309], Reich [509] and Husain and Sehgal [283] and others. This section ends with a recent fixed point theorem due to Caristi [128, 129]. Caristi’s theorem finds many applications in the field of nonlinear functional analysis.

Suggested Citation

  • Hemant Kumar Pathak, 2018. "Fixed Point Theorems," Springer Books, in: An Introduction to Nonlinear Analysis and Fixed Point Theory, chapter 0, pages 231-448, Springer.
    • Handle: RePEc:spr:sprchp:978-981-10-8866-7_5
    DOI: 10.1007/978-981-10-8866-7_5
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