Related papers: Some inequalities for the beta function and its ra…
This paper studies the connections between the zeros and their distribution functions for two particular Dirichlet $L$ functions: the Riemann zeta function, and the Catalan beta function, also known as the Dirichlet beta function. It is…
Some inequalities for functions of bounded variation that provide reverses for the inequality between the integral mean and the p-norm are established. Applications related to the celebrated Landau inequality between the norms of the…
We present a short proof of a conjecture proposed by I. Ra\c{s}a (2017), which is an inequality involving basic Bernstein polynomials and convex functions. This proof was given in the letter to I. Ra\c{s}a (2017). The methods of our proof…
We prove some basic properties of quasinearly subharmonic functions and quasinearly subharmonic functions in the narrow sense.
We prove some properties of completely monotonic functions and apply them to obtain results on gamma and $q$-gamma 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…
We review recent results on functional inequalities for systems of orthonormal functions. The key finding is that for various operators the orthonormality leads to a gain over a simple application of the triangle inequality. The operators…
This is a survey paper concerning some theorems on stochastic convex ordering and their applications to functional inequalities for convex functions. We present the recent results on those subjects
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, several complete monotonicity of functions involving ratios of two gamma or $q$-gamma…
In this paper, one new classes of convex functions which is called MT-convex functions are given. We also establish some Hadamard-type inequalities.
We review some convexity inequalities for Hermitian matrices an add one more to the list.
This paper generalizes beta divergence beyond its classical form associated with power variance functions of Tweedie models. Generalized form is represented by a compact definite integral as a function of variance function of the…
In this paper, a new lemma is proved and inequalities of Simpson type are established for co-ordinated convex functions and bounded functions.
In this paper we established new integral inequalities which are more general results for coordinated convex functions on the coordinates by using some classical inequalities.
This paper is divided into two independent parts. The first part presents new integral and series representations of the Riemaan zeta function. An equivalent formulation of the Riemann hypothesis is given and few results on this formulation…
We discuss the inequalities for $q$-integrals because of the fact that the inequalities can be very useful in the future mathematical research. Since $q$-integral of a function over an interval $[a,b]$ is defined by the difference of two…
We present inequalities and some applications to Kellers' limit and Carlemans' inequality.
We first prove some weighted inequalities for compositions of functions on time scales which are in turn applied to establish some new dynamic Opial-type inequalities in several variables. Some generalizations and applications to partial…
This is an expository note on useful expressions for the density function of a product of independent random variables where each variable has a Beta distribution.
We give a stability version of of the Blaschke-Santal\'{o} inequality in the plane.