Convex-like inequality, homogeneity, subadditivity, and a characterization of $L^p$-norm

Janusz Matkowski; Marek Pycia

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Displaying similar documents to “Convex-like inequality, homogeneity, subadditivity, and a characterization of $L^{p}$ -norm”

Subadditive functions and partial converses of Minkowski's and Mulholland's inequalities

J. Matkowski, T. Świątkowski (1993)

Fundamenta Mathematicae

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Let ϕ be an arbitrary bijection of $ℝ_{+}$ . We prove that if the two-place function $ϕ^{- 1} [ϕ (s) + ϕ (t)]$ is subadditive in $ℝ_{+}^{2}$ then $ϕ$ must be a convex homeomorphism of $ℝ_{+}$ . This is a partial converse of Mulholland’s inequality. Some new properties of subadditive bijections of $ℝ_{+}$ are also given. We apply the above results to obtain several converses of Minkowski’s inequality.

Bounded linear regularity, strong CHIP, and CHIP are distinct properties.

Bauschke, Heinz H., Borwein, Jonathan M., Tseng, Paul (2000)

Journal of Convex Analysis

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The Mazur intersection property for families of closed bounded convex sets in Banach spaces

Pradipta Bandyopadhyaya (1992)

Colloquium Mathematicae

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Plurisubharmonic saddles

Siegfried Momm (1996)

Annales Polonici Mathematici

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A certain linear growth of the pluricomplex Green function of a bounded convex domain of $ℂ^{N}$ at a given boundary point is related to the existence of a certain plurisubharmonic function called a “plurisubharmonic saddle”. In view of classical results on the existence of angular derivatives of conformal mappings, for the case of a single complex variable, this allows us to deduce a criterion for the existence of subharmonic saddles.

Existence of a continuous solution of parametric nonlinear equation with constraints.

Chabi, El Hassan, Zouaki, Hamid (2000)

Journal of Convex Analysis

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Elements of quasiconvex subdifferential calculus.

Penot, Jean-Paul, Zălinescu, Constantin (2000)

Journal of Convex Analysis

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On a Theorem of Mierczyński

Gerd Herzog (1998)

Colloquium Mathematicae

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We prove that the initial value problem x’(t) = f(t,x(t)), $x (0) = x_{1}$ is uniquely solvable in certain ordered Banach spaces if f is quasimonotone increasing with respect to x and f satisfies a one-sided Lipschitz condition with respect to a certain convex functional.

Some problems about the limit of a real-valued function

Dimitrije Hajduković (2002)

Kragujevac Journal of Mathematics

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Growth of the product $\prod_{j = 1}^{n} (1 - x^{a_{j}})$

J. P. Bell, P. B. Borwein, L. B. Richmond (1998)

Acta Arithmetica

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We estimate the maximum of $\prod_{j = 1}^{n} | 1 - x^{a_{j}} |$ on the unit circle where 1 ≤ a₁ ≤ a₂ ≤ ... is a sequence of integers. We show that when $a_{j}$ is $j^{k}$ or when $a_{j}$ is a quadratic in j that takes on positive integer values, the maximum grows as exp(cn), where c is a positive constant. This complements results of Sudler and Wright that show exponential growth when $a_{j}$ is j. In contrast we show, under fairly general conditions, that the maximum is less than $2^{n} / n^{r}$ , where r is an arbitrary positive number. One consequence...

On majorization, favard and Berwald inequalities.

Latif, Naveed, Pečarić, J., Perić, I. (2011)

Annals of Functional Analysis (AFA) [electronic only]

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Separation theorem with respect to sub-topical functions and abstract convexity.

Alimohammady, M., Shahmari, A. (2009)

The Journal of Nonlinear Sciences and its Applications

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Remarks on Lipschitzian mappings and some fixed point theorems.

Matkowski, Janusz (2007)

Banach Journal of Mathematical Analysis [electronic only]

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On ergodicity of some cylinder flows

Krzysztof Frączek (2000)

Fundamenta Mathematicae

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We study ergodicity of cylinder flows of the form $T_{f} : T \times ℝ \to T \times ℝ$ , $T_{f} (x, y) = (x + α, y + f (x))$ , where $f : T \to ℝ$ is a measurable cocycle with zero integral. We show a new class of smooth ergodic cocycles. Let k be a natural number and let f be a function such that $D^{k} f$ is piecewise absolutely continuous (but not continuous) with zero sum of jumps. We show that if the points of discontinuity of $D^{k} f$ have some good properties, then $T_{f}$ is ergodic. Moreover, there exists $ε_{f} > 0$ such that if $v : T \to ℝ$ is a function with zero integral such that $D^{k} v$ is of bounded...

Displaying similar documents to “Convex-like inequality, homogeneity, subadditivity, and a characterization of L p -norm”

Displaying similar documents to “Convex-like inequality, homogeneity, subadditivity, and a characterization of $L^{p}$ -norm”