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Monotone Operators, Strongly $$\phi $$ ϕ -Accretive Operators and Their Variants

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 this chapter, we introduce the reader to the theory of monotone operators, $$\phi $$ ϕ -accretive operators and their generalizations. The concept of monotone operator was first introduced by Minty in his paper of 1962, Minty, Duke Math J 29:341–346, 1962, [400], wherein he gave a surjectivity theorem for such operators. Since then, this theory is widely developed and has found useful applications in the investigation of the solvability of nonlinear operator equations and in particular of partial differential equations and integral equations. Our purpose is to give a systematic treatment (with historical development) of various topics in the theory of monotone operators needed for such an investigation.

Suggested Citation

  • Hemant Kumar Pathak, 2018. "Monotone Operators, Strongly $$\phi $$ ϕ -Accretive Operators and Their Variants," Springer Books, in: An Introduction to Nonlinear Analysis and Fixed Point Theory, chapter 0, pages 177-230, Springer.
    • Handle: RePEc:spr:sprchp:978-981-10-8866-7_4
    DOI: 10.1007/978-981-10-8866-7_4
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