Taiwanese Journal of Mathematics


Szilárd László

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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.

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

First available in Project Euclid: 18 July 2017

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

generalized monotone operator maximal monotonicity locally monotone operator generalized convex function


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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