Related papers: Approximations of generalized Bernstein functions
We investigate subclasses of generalized Bernstein functions related to complete Bernstein and Thorin-Bernstein functions. Representations in terms of incomplete beta and gamma as well as hypergeometric functions are presented. Several…
In the paper, the authors establish an inequality involving exponential functions and sums, introduce a ratio of many gamma functions, discuss properties, including monotonicity, logarithmic convexity, (logarithmically) complete…
In this article, we define a special function called the Bigamma function. It provides a generalization of Euler's gamma function. Several algebraic properties of this new function are studied. In particular, results linking this new…
In this paper, we investigate the complete monotonicity of some functions involving gamma function. Using the monotonic properties of these functions, we derived some inequalities involving gamma and beta functions. Such inequalities…
Recently, extensions of gamma and beta functions have been studied by many researchers due to their nice properties and variety of applications in different fields of science. The aim of this note is to investigate generalized inequalities…
We introduce new generalizations of the Gamma and the Beta functions. Their properties are investigated and known results are obtained as particular cases.
We prove that certain functions involving ratios of Gamma functions and the Psi-function belong to generalized Bernstein classes and new properties of generalized Bernstein functions are given.
In this paper, we present some double inequalities involving certain ratios of the Gamma function. These results are further generalizations of several previous results. The approach is based on the monotonicity properties of some functions…
Motivated mainly by certain interesting recent extensions of the Gamma, Beta and hypergeometric functions, we introduce here new extensions of the Beta function, hypergeometric and confluent hypergeometric functions. We systematically…
In this paper, we introduce a new two-parameter deformation of the Gamma function that generalizes some existing Gamma-type functions in the literature. We study properties of this function that depend on the parameters. We also prove some…
The logarithmic convexity of restrictions of the Beta functions to rays parallel to the main diagonal and the functional equation \[ \phi\left( x+1\right) =\frac{x\left( x+k\right) }{\left( 2x+k+1\right) \left( 2x+k\right) }\phi\left(…
In the paper, the authors review origins, motivations, and generalizations of a series of inequalities involving several exponential functions and sums, establish three new inequalities involving finite exponential functions and sums by…
In this paper, we present some new inequalities for the gamma function. The main tools are the multiple-correction method developed in our previous works, and a generalized Mortici's lemma.
We calculate some infinite sums containing the digamma function in closed-form. These sums are related either to the incomplete beta function or to the Bessel functions. The calculations yield interesting new results as by-products, such as…
A new type of combinations of Bernstein operators is given in [1]. Here, we introduce another one, which can be used to approximate the functions with singularities. The direct and inverse results of the weighted approximation of this new…
In this paper, additional properties of the lower gamma functions and the error functions are introduced and proven. In particular, we prove interesting relations between the error functions and Laplace transform.
In the paper, the authors establish three kinds of double inequalities for the trigamma function in terms of the exponential function to powers of the digamma function. These newly established inequalities extend some known results. The…
We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the…
Recently, it has been shown by Ighachanea and Akkouchia \cite{0.1} that using binomial coefficients, one can derive some new refinements of Holder's inequalities. This inequalities then can be applied to a wide class of special functions…
We prove a matrix trace inequality for completely monotone functions and for Bernstein functions. As special cases we obtain non-trivial trace inequalities for the power function x->x^q, which for certain values of q complement McCarthy's…