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Journal of Convex Analysis 18 (2011), No. 1, 259--275
Copyright Heldermann Verlag 2011

An Abstract Convex Representation of Maximal Abstract Monotone Operators

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

Andrew C. Eberhard
School of Mathematical and Geospatial Sciences, RMIT University, Melbourne, Victoria 3001, Australia

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.

Keywords: Monotone operator, abstract monotonicity, abstract convex function, abstract convexity, IPH function.

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

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