The use of conjugate convex functions in complex analysis
Christer Kieselman (1983)
Banach Center Publications
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Christer Kieselman (1983)
Banach Center Publications
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Zoltán M. Balogh, Matthieu Rickly (2003)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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We discuss differentiability properties of convex functions on Heisenberg groups. We show that the notions of horizontal convexity (h-convexity) and viscosity convexity (v-convexity) are equivalent and that h-convex functions are locally Lipschitz continuous. Finally we exhibit Weierstrass-type h-convex functions which are nowhere differentiable in the vertical direction on a dense set or on a Cantor set of vertical lines.
T. Zgraja (2005)
Acta Universitatis Carolinae. Mathematica et Physica
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Xie Ding, Kok-Keong Tan (1992)
Colloquium Mathematicae
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Ky Fan’s minimax inequality [8, Theorem 1] has become a versatile tool in nonlinear and convex analysis. In this paper, we shall first obtain a minimax inequality which generalizes those generalizations of Ky Fan’s minimax inequality due to Allen [1], Yen [18], Tan [16], Bae Kim Tan [3] and Fan himself [9]. Several equivalent forms are then formulated and one of them, the maximal element version, is used to obtain a fixed point theorem which in turn is applied to obtain an existence...
T. Lachand-Robert, M. A. Peletier (2001)
Annales de l'I.H.P. Analyse non linéaire
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Dariusz Zagrodny (1994)
Studia Mathematica
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Conditions under which the inf-convolution of f and g has the cancellation property (i.e. f □ h ≡ g □ h implies f ≡ g) are treated in a convex analysis framework. In particular, we show that the set of strictly convex lower semicontinuous functions on a reflexive Banach space such that constitutes a semigroup, with inf-convolution as multiplication, which can be embedded in the group of its quotients.