Results 21 to 30 of about 346 (88)

On the substitution rule for Lebesgue-Stieltjes integrals [PDF]

open access: yes, 2012
We show how two change-of-variables formulae for Lebesgue-Stieltjes integrals generalize when all continuity hypotheses on the integrators are dropped.
Apostol   +12 more
core   +5 more sources

On the refinements of the integral Jensen-Steffensen inequality

open access: yesJournal of Inequalities and Applications, 2013
In this paper, we present integral versions of some recently proved results which refine the Jensen-Steffensen inequality. We prove the n-exponential convexity and log-convexity of the functions associated with the linear functionals constructed from the
Sadia Khalid, J. Pečarić
semanticscholar   +2 more sources

Uniqueness of nontrivially complete monotonicity for a class of functions involving polygamma functions [PDF]

open access: yes, 2010
For $m,n\in\mathbb{N}$, let $f_{m,n}(x)=\bigr[\psi^{(m)}(x)\bigl]^2+\psi^{(n)}(x)$ on $(0,\infty)$. In the present paper, we prove using two methods that, among all $f_{m,n}(x)$ for $m,n\in\mathbb{N}$, only $f_{1,2}(x)$ is nontrivially completely ...
Abramowitz M.   +10 more
core   +1 more source

Two monotonic functions involving gamma function and volume of unit ball

open access: yes, 2010
In present paper, we prove the monotonicity of two functions involving the gamma function $\Gamma(x)$ and relating to the $n$-dimensional volume of the unit ball $\mathbb{B}^n$ in $\mathbb{R}^n$.Comment: 7 ...
Anderson G. D.   +12 more
core   +1 more source

Complete monotonicity properties of functions involving q-gamma and q-digamma functions

open access: yes, 2014
In this paper, the q -analogue of the Stirling formula (the Moak formula) for the q gamma function is exploited to prove the complete monotonicity property of functions involving the q -gamma and the q -digamma functions.
A. Salem
semanticscholar   +1 more source

Some classes of completely monotonic functions related to q-gamma and q-digamma functions

open access: yes, 2016
In the paper, some classes of completely monotonic functions involving the q -gamma and q -digamma functions are derived. The monotonicity properties of these functions are exploited to establish a double inequality for the ratio of the q -gamma function
A. Salem
semanticscholar   +1 more source

Gaps Between Classes of Matrix Monotone Functions [PDF]

open access: yes, 2002
The class Pn(I) of matrix monotone functions of order n, defined on an open interval I, is considered in this paper. Explicit examples are given to prove that if I is different from the whole real line, then Pn+1(I) is a proper subset of Pn(I) for each ...
Frank Hansen, Guoxing Ji, J. Tomiyama
semanticscholar   +1 more source

A certain class of completely monotonic sequences

open access: yesAdvances in Differential Equations, 2013
In this article, we present some necessary conditions, a sufficient condition and a necessary and sufficient condition for sequences to be completely monotonic. One counterexample is also presented.MSC:40A05, 26A45, 26A48, 39A60.
Senlin Guo, H. Srivastava, Necdet Batır
semanticscholar   +2 more sources

Rearrangements of general monotone functions and of their Fourier transforms

open access: yes, 2018
We extend further Boas’ conjecture concerning functions nonincreasing on (0,∞) and their Fourier transforms by considering rearrangements of general monotone functions and of their Fourier transforms.
Barry Booton
semanticscholar   +1 more source

An alternative proof of Elezovi\'c-Giordano-Pe\v{c}ari\'c's theorem

open access: yes, 2009
In the present note, an alternative proof is supplied for Theorem~1 in [N. Elezovi\'c, C. Giordano and J. Pe\v{c}ari\'c, \textit{The best bounds in Gautschi's inequality}, Math. Inequal. Appl.
Guo, Bai-Ni, Qi, Feng
core   +1 more source

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