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Displaying 341 – 360 of 687

Modified log-Sobolev inequalities for convex functions on the real line. Sufficient conditions

Radosław Adamczak, Michał Strzelecki (2015)

Studia Mathematica

We provide a mild sufficient condition for a probability measure on the real line to satisfy a modified log-Sobolev inequality for convex functions, interpolating between the classical log-Sobolev inequality and a Bobkov-Ledoux type inequality. As a consequence we obtain dimension-free two-level concentration results for convex functions of independent random variables with sufficiently regular tail decay. We also provide a link between modified log-Sobolev inequalities...

Mond-Weir duality in vector programming with generalized invex functions on differentiable manifolds.

Ferrara, Massimiliano, Mititelu, Ştefan (2006)

Balkan Journal of Geometry and its Applications (BJGA)

Monotone Valuations on the Space of Convex Functions

L. Cavallina, A. Colesanti (2015)

Analysis and Geometry in Metric Spaces

We consider the space Cn of convex functions u defined in Rn with values in R ∪ {∞}, which are lower semi-continuous and such that lim|x| } ∞ u(x) = ∞. We study the valuations defined on Cn which are invariant under the composition with rigid motions, monotone and verify a certain type of continuity. We prove integral representations formulas for such valuations which are, in addition, simple or homogeneous.

More than first-order developments of convex functions: primal-dual relations.

Lemaréchal, C., Sagastizábel, C. (1996)

Journal of Convex Analysis

Multidimensional extension of L. C. Young's inequality.

Towghi, Nasser (2002)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Multifunctions with selections of convex and concave type.

Nikodem, Kazimierz, Páles, Zsolt, Wa̧sowicz, Szymon (2000)

Mathematica Pannonica

Multiple integrals evaluated by functional equations

Shigeru Haruki (1973)

Annales Polonici Mathematici

Multiple Lebesgue integration on time scales.

Bohner, Martin, Guseinov, Gusein Sh. (2006)

Advances in Difference Equations [electronic only]

Multivariate version of a Jensen-type inequality.

Agnew, Robert A. (2005)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Názorné vysvětlování kapitoly o parciálních derivacích složené funkce

Robert Karpe (1963)

Pokroky matematiky, fyziky a astronomie

Necessary and sufficient conditions for a curve to be the gradient range of a $C^{1}$ -smooth function.

Korobkov, M.V., Panov, E.Yu. (2007)

Sibirskij Matematicheskij Zhurnal

Necessary and sufficient conditions for the chain rule in $W_{loc}^{1, 1} (ℝ^{N}; ℝ^{d})$ and $B V_{loc} (ℝ^{N}; ℝ^{d})$

Giovanni Leoni, Massimiliano Morini (2007)

Journal of the European Mathematical Society

We prove necessary and sufficient conditions for the validity of the classical chain rule in the Sobolev space $W_{loc}^{1, 1} (ℝ^{N}; ℝ^{d})$ and in the space $B V_{loc} (ℝ^{N}; ℝ^{d})$ of functions of bounded variation.

Necessary conditions for Lipschitz continuous discrete control problems

Jaroslav Doležal (1985)

Banach Center Publications

New variants of Khintchine's inequality.

Ioan Serb (2001)

Collectanea Mathematica

Variants of Khintchine's inequality with coefficients depending on the vector dimension are proved. Equality is attained for different types of extremal vectors. The Schur convexity of certain attached functions and direct estimates in terms of the Haagerup type of functions are also used.

Non-compact lamination convex hulls

Jan Kolář (2003)

Annales de l'I.H.P. Analyse non linéaire

Nonconvex Lipschitz function in plane which is locally convex outside a discontinuum

Dušan Pokorný (2014)

Commentationes Mathematicae Universitatis Carolinae

We construct a Lipschitz function on $ℝ^{2}$ which is locally convex on the complement of some totally disconnected compact set but not convex. Existence of such function disproves a theorem that appeared in a paper by L. Pasqualini and was also cited by other authors.

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