Abstract

We develop a theory of monotone operators in the framework of abstract convexity. We present a definition for abstract monotone operators and some examples of an abstract convex function such that its subdifferential is a maximal abstract monotone operator. Finally, we give an abstract convex representation for maximal abstract monotone operators.

Author information

Contact details are reproduced from the original publication and may be historical.

H. Mohebi

Mahani Mathematical Research Center and Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran

hmohebi@mail.uk.ac.ir

Andrew C. Eberhard

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

andy.eb@rmit.edu.au

Keywords

  • Monotone operator
  • abstract monotonicity
  • abstract convex function
  • abstract convexity
  • IPH function

Mathematics Subject Classification

47H05, 47H04, 52A01, 26A48, 26A51

Suggested citation

H. Mohebi, A. C. Eberhard. “An Abstract Convex Representation of Maximal Abstract Monotone Operators.” Journal of Convex Analysis 18 (2011), No. 1, 259–275. https://doi.org/10.68381/jca18014

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Published by Heldermann Verlag, 2011. Rights now held by Banach Press.