Related papers: Some inequalities for the beta function and its ra…
In this paper, we establish some integral ineuqalities for n- times differentiable quasi-convex functions.
In this paper, we prove an inequality regarding the differential polynomial. This improves some recent results.
In this paper, the authors establish some inequalities involving the Psi and $k$-Gamma functions. The procedure utilizes some monotonicity properties of some functions associated with the Psi and $k$-Gamma functions.
In this paper, new inequalities connected with the celebrated Steffensen's integral inequality are proved.
In this expository and survey paper, along one of main lines of bounding the ratio of two gamma functions, we look back and analyse some inequalities, the complete monotonicity of several functions involving ratios of two gamma or $q$-gamma…
In this paper we present 43 new inequalities related to integer part and fractional part.
We obtain simple proofs of certain inequalites for bivariate means.
The classical beta function B(x; y) is one of the most fundamental special functions, due to its important role in various fields in the mathematical, physical, engineering and statistical sciences. Useful extensions of the classical Beta…
In this paper we investigate the monotonicity properties related to the ratio of gamma functions, from which some related asymptotics and inequalities are established. Some special cases also confirm the conjectures of C.-P. Chen…
All beta-type functions, which are p-homogeneous, are determined. Applying this result, we show that a beta-type function is a homogeneous mean iff it is the harmonic one. A reformulation of a result due to Heuvers in terms of a Cauchy…
In the paper, we present a monotonicity result of a function involving the gamma function and the logarithmic function, refine a double inequality for the gamma function, and improve some known results for bounding the gamma function.
For a wide range of pairs of mixed norm spaces such that one space is contained in another, we characterize all cases when contractive norm inequalities hold. In particular, this yields such results for many pairs of weighted Bergman…
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…
This article offers different proofs of ten inequalities from those already published. So that the readers can see for themselves, the tasks specified in the condition of the source and classical inequalities which used in previously…
This paper studies the log-convexity of the extended beta functions. As a consequence, Tur\'an-type inequalities are established.The monotonicity, log-convexity, log-concavity of extended hypergeometric functions are deduced by using the…
The Bregman divergence have been the subject of several studies. We do not go to do an exhaustive study of its subclasses, but propose a proof that shows that the \b{eta}-divergence are subclasses of the Bregman divergences. It is in this…
In this article we study the differentiability of Mather's $\beta$-function on closed surfaces and its relation to the integrability of the system.
A simple closed-form approximation for the median of the beta distribution Beta(a, b) is introduced: (a-1/3)/(a+b-2/3) for (a,b) both larger than 1 has a relative error of less than 4%, rapidly decreasing to zero as both shape parameters…
In this note we prove optimal inequalities for bounded functions in terms of their deviation from their mean. These results extend and generalize some known inequalities due to Thong (2011) and Perfetti (2011)
Some inequalities for different types of convexity are established.