Displaying similar documents to “Subdifferential characterization of quasiconvexity and convexity.”

Abstract Subdifferential Calculus and Semi-Convex Functions

Ivanov, Milen, Zlateva, Nadia (1997)

Serdica Mathematical Journal

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∗ The work is partially supported by NSFR Grant No MM 409/94. We develop an abstract subdifferential calculus for lower semicontinuous functions and investigate functions similar to convex functions. As application we give sufficient conditions for the integrability of a lower semicontinuous function.

When some variational properties force convexity

M. Volle, J.-B. Hiriart-Urruty, C. Zălinescu (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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The notion of adequate (resp. strongly adequate) function has been recently introduced to characterize the essentially strictly convex (resp. essentially firmly subdifferentiable) functions among the weakly lower semicontinuous (resp. lower semicontinuous) ones. In this paper we provide various necessary and sufficient conditions in order that the lower semicontinuous hull of an extended real-valued function on a reflexive Banach space is essentially strictly convex. Some new results...

Generalized midconvexity

Jacek Tabor, Józef Tabor, Krzysztof Misztal (2013)

Banach Center Publications

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There are many types of midconvexities, for example Jensen convexity, t-convexity, (s,t)-convexity. We provide a uniform framework for all the above mentioned midconvexities by considering a generalized middle-point map on an abstract space X. We show that we can define and study the basic convexity properties in this setting.

On the radius of convexity for a class of conformal maps

V. Karunakaran, K. Bhuvaneswari (2007)

Colloquium Mathematicae

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Let 𝓐 denote the class of all analytic functions f in the open unit disc 𝔻 in the complex plane satisfying f(0) = 0, f'(0) = 1. Let U(λ) (0 < λ ≤ 1) denote the class of functions f ∈ 𝓐 for which |(z/f(z))²f'(z) -1| < λ for z ∈ 𝔻. The behaviour of functions in this class has been extensively studied in the literature. In this paper, we shall prove that no member of U₀(λ) = {f ∈ U(λ): f''(0) = 0} is convex in 𝔻 for any λ and obtain a lower bound...