Displaying similar documents to “Generalizations of some classical inequalities and their applications”

Comparison theorems of isoperimetric type for moments of compact sets.

F. G. Avkhadiev, I. R. Kayumov (2004)

Collectanea Mathematica

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A unified approach to prove isoperimetric inequalities for moments and basic inequalities of interpolation spaces L(p,q) is developed. Instead symmetrization methods we use a monotonicity property of special Stiltjes' means.

The converse of the Hölder inequality and its generalizations

Janusz Matkowski (1994)

Studia Mathematica

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Let (Ω,Σ,μ) be a measure space with two sets A,B ∈ Σ such that 0 < μ (A) < 1 < μ (B) < ∞ and suppose that ϕ and ψ are arbitrary bijections of [0,∞) such that ϕ(0) = ψ(0) = 0. The main result says that if ʃ Ω x y d μ ≤ ϕ - 1 ( ʃ Ω ϕ ∘ x d μ ) ψ - 1 ( ʃ Ω ψ ∘ x d μ ) for all μ-integrable nonnegative step functions x,y then ϕ and ψ must be conjugate power functions. If the measure space (Ω,Σ,μ) has one of the following properties: (a) μ (A) ≤ 1 for every A ∈ Σ of finite measure; (b) μ (A) ≥ 1 for every A ∈ Σ of positive measure, then...

Integral Inequalities and Applications to Partial Differential Equations with “Maxima” Интегрални неравенства и приложения в частните диференциални уравнения с “максимуми”

Stefanova, Kremena (2011)

Union of Bulgarian Mathematicians

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Кремена В. Стефанова - В тази статия са разрешени някои нелинейни интегрални неравенства, които включват максимума на неизвестната функция на две променливи. Разгледаните неравенства представляват обобщения на класическото неравенство на Гронуол-Белман. Значението на тези интегрални неравенства се определя от широките им приложения в качествените изследвания на частните диференциални уравнения с “максимуми” и е илюстрирано чрез някои директни приложения. This paper deals...