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$\theta-$MONOTONE OPERATORS AND $\theta-$CONVEX FUNCTIONS
- Source :
- Taiwanese J. Math. 16, no. 2 (2012), 733-759
- Publication Year :
- 2012
- Publisher :
- Mathematical Society of the Republic of China, 2012.
-
Abstract
- In this paper we introduce a new monotonicity concept for multivalued operators, respectively, a new convexity concept for real valued functions, which generalize several monotonicity, respectively, convexity notions already known in literature. We present some fundamental properties of the operators having this monotonicity property. We show that if such a monotonicity property holds locally then the same property holds globally on the whole domain of the operator. We also show that these two new concepts are closely related. As an immediate application we furnish some surjectivity results in finite dimensional spaces.
- Subjects :
- Discrete mathematics
TheoryofComputation_MISCELLANEOUS
Property (philosophy)
locally monotone operator
generalized monotone operator
47H05
General Mathematics
Monotonic function
Convexity
Domain (mathematical analysis)
26B25
Monotone polygon
Operator (computer programming)
49J50
generalized convex function
26A51
maximal monotonicity
Convex function
Mathematics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Taiwanese J. Math. 16, no. 2 (2012), 733-759
- Accession number :
- edsair.doi.dedup.....94aa7d693bf307c7c4caf73c3477b36f