Convergence of Ratios and Differences of two Order Statistics
Convergence of series of dilated functions and spectral norms of GCD matrices
We establish a connection between the L² norm of sums of dilated functions whose jth Fourier coefficients are 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
Convergence theorems for a Daniell-Loomis integral.
Convergence theorems for the Perron integral and Sklyarenko's condition
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
We give a definition of uniform PU-integrability for a sequence of -measurable real functions defined on an abstract metric space and prove that it is not equivalent to the uniform -integrability.
Convergences for the group of real numbers
Convergencia de sucesiones dadas por fórmulas de recurencia de primer orden
Convex functions and the Hadamard inequality.
Convex functions of higher orders in Euclidean spaces
Convex functions with respect to logarithmic mean and ѕandwich theorem
Convex transformations with Banach lattice range.
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
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.
Convexity properties and inequalities for a generalized gamma function.
Convexity with given infinite weight sequences.
Convex-like inequality, homogeneity, subadditivity, and a characterization of -norm
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 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 -norm.
Convolution Products in L1(R+), Integral Transforms and Fractional Calculus
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.
Convolutions and Mean Square Estimates of Certain Number-theoretic Error Terms
Convolutions with the continuous primitive integral.