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Maximal Abstract Monotonicity and Generalized Fenchel’s Conjugation Formulas

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Abstract

In this paper, we present a generalization of a theory of monotone operators in the framework of abstract convexity. We show that how generalized Fenchel’s conjugation formulas can be used to obtain some results on maximal abstract monotonicity. We give a necessary and sufficient condition for maximality of abstract monotone operators representable by abstract convex functions by using an additivity constraint qualification.

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Authors and Affiliations

  1. School of Mathematical and Geospatial Sciences, RMIT University, Melbourne, Victoria, 3001, Australia

    A. C. Eberhard & Hossein Mohebi

  2. Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran

    Hossein Mohebi

Authors
  1. A. C. Eberhard
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  2. Hossein Mohebi
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Correspondence to Hossein Mohebi.

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Eberhard, A.C., Mohebi, H. Maximal Abstract Monotonicity and Generalized Fenchel’s Conjugation Formulas. Set-Valued Anal 18, 79–108 (2010). https://doi.org/10.1007/s11228-009-0124-1

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  • DOI: https://doi.org/10.1007/s11228-009-0124-1

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