Taiwanese Journal of Mathematics

$\theta-$MONOTONE OPERATORS AND $\theta-$CONVEX FUNCTIONS

Szilárd László

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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.

Article information

Source
Taiwanese J. Math., Volume 16, Number 2 (2012), 733-759.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406612

Digital Object Identifier
doi:10.11650/twjm/1500406612

Mathematical Reviews number (MathSciNet)
MR2892909

Zentralblatt MATH identifier
1262.47075

Subjects
Primary: 47H05: Monotone operators and generalizations 26A51: Convexity, generalizations 26B25: Convexity, generalizations 49J50: Fréchet and Gateaux differentiability [See also 46G05, 58C20]

Keywords
generalized monotone operator maximal monotonicity locally monotone operator generalized convex function

Citation

László, Szilárd. $\theta-$MONOTONE OPERATORS AND $\theta-$CONVEX FUNCTIONS. Taiwanese J. Math. 16 (2012), no. 2, 733--759. doi:10.11650/twjm/1500406612. https://projecteuclid.org/euclid.twjm/1500406612


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