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.

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.

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.

Growth of the product ∏ 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 ∏ 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 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 × ℝ → T × ℝ , T f ( x , y ) = ( x + α , y + f ( x ) ) , where f : T → 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 → ℝ is a function with zero integral such that D k v is of bounded...