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Displaying 81 – 100 of 109

Controlled convergence theorems for Henstock-Kurzweil-Pettis integral on $m$ -dimensional compact intervals

Sokol B. Kaliaj, Agron D. Tato, Fatmir D. Gumeni (2012)

Czechoslovak Mathematical Journal

In this paper we use a generalized version of absolute continuity defined by J. Kurzweil, J. Jarník, Equiintegrability and controlled convergence of Perron-type integrable functions, Real Anal. Exch. 17 (1992), 110–139. By applying uniformly this generalized version of absolute continuity to the primitives of the Henstock-Kurzweil-Pettis integrable functions, we obtain controlled convergence theorems for the Henstock-Kurzweil-Pettis integral. First, we present a controlled convergence theorem for...

Convergence of ap-Henstock-Kurzweil integral on locally compact spaces

Hemanta Kalita, Ravi P. Agarwal, Bipan Hazarika (2025)

Czechoslovak Mathematical Journal

We introduce an ap-Henstock-Kurzweil type integral with a non-atomic Radon measure and prove the Saks-Henstock type lemma. The monotone convergence theorem, $μ_{ap}$ -Henstock-Kurzweil equi-integrability, and uniformly strong Lusin condition are discussed.

Convergence of Ratios and Differences of two Order Statistics

Jef L. Teugels, Giovanni Vanroelen (2002)

Publications de l'Institut Mathématique

Convergence of series of dilated functions and spectral norms of GCD matrices

Christoph Aistleitner, István Berkes, Kristian Seip, Michel Weber (2015)

Acta Arithmetica

We establish a connection between the L² norm of sums of dilated functions whose jth Fourier coefficients are $(j^{- α})$ for some α ∈ (1/2,1), and the spectral norms of certain greatest common divisor (GCD) matrices. Utilizing recent bounds for these spectral norms, we obtain sharp conditions for the convergence in L² and for the almost everywhere convergence of series of dilated functions.

Convergence presque sûre de moyennes de sommes de Riemann

Jean-Jacques Ruch (1998)

Acta Arithmetica

Convergence theorems for a Daniell-Loomis integral.

Günzler, H. (1991)

Mathematica Pannonica

Convergence theorems for the Perron integral and Sklyarenko's condition

Štefan Schwabik (1992)

Commentationes Mathematicae Universitatis Carolinae

It is shown that a uniform version of Sklyarenko's integrability condition for Perron integrals together with pointwise convergence of a sequence of integrable functions are sufficient for a convergence theorem for Perron integrals.

Convergence theorems for the PU-integral

Giuseppa Riccobono (2000)

Mathematica Bohemica

We give a definition of uniform PU-integrability for a sequence of $μ$ -measurable real functions defined on an abstract metric space and prove that it is not equivalent to the uniform $μ$ -integrability.

Convergences $𝔏_{S}^{H}$ for the group of real numbers

Josef Novák (1993)

Czechoslovak Mathematical Journal

Convergencia de sucesiones dadas por fórmulas de recurencia de primer orden

Yu Takeuchi (1993)

Revista colombiana de matematicas

Convex functions and the Hadamard inequality.

Azpeitia, Alfonso G. (1994)

Revista Colombiana de Matemáticas

Convex functions of higher orders in Euclidean spaces

Roman Ger (1972)

Annales Polonici Mathematici

Convex functions with respect to logarithmic mean and ѕandwich theorem

Zygfryd Kominek, T. Zgraja (1999)

Acta Universitatis Carolinae. Mathematica et Physica

Convex transformations with Banach lattice range.

Roman Ger (1987)

Stochastica

A closed epigraph theorem for Jensen-convex mappings with values in Banach lattices with a strong unit is established. This allows one to reduce the examination of continuity of vector valued transformations to the case of convex real functionals. In particular, it is shown that a weakly continuous Jensen-convex mapping is continuous. A number of corollaries follow; among them, a characterization of continuous vector-valued convex transformations is given that answers a question raised by Ih-Ching...

Convexity and almost convexity in groups

Witold Jarczyk (2013)

Banach Center Publications

We give a review of results proved and published mostly in recent years, concerning real-valued convex functions as well as almost convex functions defined on a (not necessarily convex) subset of a group. Analogues of such classical results as the theorems of Jensen, Bernstein-Doetsch, Blumberg-Sierpiński, Ostrowski, and Mehdi are presented. A version of the Hahn-Banach theorem with a convex control function is proved, too. We also study some questions specific for the group setting, for instance...

Convexity of the zero-balanced Gaussian hypergeometric functions with respect to Hölder means.

Baricz, Árpád (2007)

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

Convexity properties and inequalities for a generalized gamma function.

Krasniqi, Valmir, Shabani, Armend Sh. (2010)

Applied Mathematics E-Notes [electronic only]

Convexity with given infinite weight sequences.

Zoltán Daróczy, Zsolt Páles (1987)

Stochastica

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

Janusz Matkowski, Marek Pycia (1995)

Annales Polonici Mathematici

Let a and b be fixed real numbers such that 0 < mina,b < 1 < a + b. We prove that every function f:(0,∞) → ℝ satisfying f(as + bt) ≤ af(s) + bf(t), s,t > 0, and such that $l i m s u p_{t \to 0 +} f (t) \leq 0$ must be of the form f(t) = f(1)t, t > 0. This improves an earlier result in [5] where, in particular, f is assumed to be nonnegative. Some generalizations for functions defined on cones in linear spaces are given. We apply these results to give a new characterization of the $L^{p}$ -norm.

Convolution Products in L1(R+), Integral Transforms and Fractional Calculus

Miana, Pedro (2005)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 43A20, 26A33 (main), 44A10, 44A15We prove equalities in the Banach algebra L1(R+). We apply them to integral transforms and fractional calculus.* Partially supported by Project BFM2001-1793 of the MCYT-DGI and FEDER and Project E-12/25 of D.G.A.

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