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

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

Chapter Chapter 4 in An Introduction to Nonlinear Analysis and Fixed Point Theory, 2018, pp 177-230 from Springer

Abstract: 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.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-10-8866-7_4

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DOI: 10.1007/978-981-10-8866-7_4

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