Related papers: The logarithmic Cauchy quotient mean
Let $a=(a_1,a_2,...c,a_n)$ for $n\in\mathbb{N}$ be a given sequence of positive numbers. In the paper, the authors establish, by using Cauchy's integral formula in the theory of complex functions, an integral representation of the principal…
The notion of pairable functions is introduced and some of its properties are developed. In this connection the famous Euler identity is interpreted as a property of certain pairable functions and finite cyclic groups.
We introduce new generalizations of the Gamma and the Beta functions. Their properties are investigated and known results are obtained as particular cases.
We derive new reduction formulas for the incomplete beta function and the Lerch transcendent in terms of elementary functions. As an application, we calculate some new integrals. Also, we use these reduction formulas to test the performance…
The main objective of the present paper is to solve the several long standing divergence problems related to the logarithmic means of Fourier series in context of general orthonormal systems.
The main goal of this paper is to show that if a real valued function defined on a groupoid satisfies a certain Levi--Civita-type functional equation, then it also fulfills a Cauchy--Schwarz-type functional inequality. In particular, if the…
In this paper we present several new classes of logarithmically completely monotonic functions. Our functions have in common that they are defined in terms of the $q-$gamma and $q-$digamma functions. As an applications of this results, some…
In this work we present a new, natural, definition for the mean width of log-concave functions. We show that the new definition coincide with a previous one by B. Klartag and V. Milman, and deduce some properties of the mean width,…
In a previous paper we have presented a new method for solving a class of Cauchy integral equations. In this work we discuss in detail how to manage this method numerically, when only a finite and noisy data set is available: particular…
The beta distribution is a two-parameter family of probability distributions whose distribution function is the (regularised) incomplete beta function. In this paper, the inverse incomplete beta function is studied analytically as…
In the article, a notion "logarithmically absolutely monotonic function" is introduced, an inclusion that a logarithmically absolutely monotonic function is also absolutely monotonic is revealed, the logarithmically complete monotonicity…
In this paper, we investigate some properties of higher-order Cauchy of the second kind and poly-Cauchy of the second mixed type polynomials with umbral calculus viewpoint. From our investigation, we derive many interesting identities of…
In recent papers the convexity of quasiarithmetic means was characterized under twice differentiability assumptions. One of the main goals of this paper is to show that the convexity or concavity of a quasiarithmetic mean implies the the…
Some real functions f induce mean of positive numbers and the matrix monotonicity gives a possibility for means of positive definite matrices. Moreover, such a function f can define linear mapping beta on matrices (which is basic in the…
We consider power means of independent and identically distributed (i.i.d.) non-integrable random variables. The power mean is an example of a homogeneous quasi-arithmetic mean. Under certain conditions, several limit theorems hold for the…
Using a probabilistic approach, we derive several interesting identities involving beta functions. Our results generalize certain well-known combinatorial identities involving binomial coefficients and gamma functions.
In the paper, the monotonicity and logarithmic convexity of Gini means and related functions are investigated.
The maximal Orlicz space such that the mixed logarithmic means of multiple Fourier series for the functions from this space converge in $L_{1}$-norm is found.
In this note, we characterize the limiting functions in mod-Gausssian convergence; our approach sheds a new light on the nature of mod-Gaussian convergence as well. Our results in fact more generally apply to mod-* convergence, where *…
Some Ostrowski type inequalities via Cauchy's mean value theorem and applications for certain particular instances of functions are given.