POSITIVELY HOMOGENEOUS FUNCTIONS
AND MAXIMAL ABSTRACT MONOTONICITY
Atefeh Mohebi1, Hossein Mohebi2
1 Department of Mathematics
Shahid Bahonar University of Kerman
Kerman, P.O. Box 76169-133, Postal Code 7616914111, IRAN
2Department of Mathematics
Shahid Bahonar University of Kerman
and Graduate University of Advanced Technology, Kerman
P.O. Box: 76169-133, Postal Code 7616914111, IRAN
Abstract. In this paper, by using a set of positively homogeneous functions, we develop a theory of monotone operators in the framework of abstract monotonicity. Indeed, by using a set of positively homogeneous functions, we give some criteria for maximal abstract monotonicity.
AMS Subject classification: 47H05, 47H04, 52A01
Keywords and phrases: positively homogeneous function, monotone operator, abstract monotonicity, abstract convexity


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DOI: 10.12732/ijam.v27i1.6

Volume: 27
Issue: 1
Year: 2014