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Operations with monotone operators and the monotonicity of the resulting operators

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Abstract

In this paper we provide estimates for the parameters of monotonicity of two composed operators as well as for the sum of two operators. The estimates are given in terms of the parameters of monotonicity of the involved operators and they produce examples of h-monotone operators which are not Minty–Browder monotone. As an application to these estimates we prove a global injectivity result.

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Acknowledgments

Cornel Pintea was supported through GSCE Grant Number 30257/22.01.2015 financed by the Babeş-Bolyai University.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Babeş-Bolyai University, M. Kogălniceanu 1, 400084, Cluj-Napoca, Romania

    Cornel Pintea

  2. Technical University of Cluj-Napoca, Memorandumului nr. 28, 400114, Cluj-Napoca, Romania

    Daniela Marian & Ioan Radu Peter

Authors
  1. Daniela Marian
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  2. Ioan Radu Peter
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  3. Cornel Pintea
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Correspondence to Ioan Radu Peter.

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Communicated by J. Escher.

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Marian, D., Peter, I.R. & Pintea, C. Operations with monotone operators and the monotonicity of the resulting operators. Monatsh Math 181, 143–168 (2016). https://doi.org/10.1007/s00605-015-0820-x

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  • DOI: https://doi.org/10.1007/s00605-015-0820-x

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