arXiv subjects
Publications and source records attributed to Valmir Krasniqi.
We characterize of the $q$-Bernstein functions in terms of $q$-Laplace transform. Moreover, we present several results of $q$-completely monotonic, $q$-log completely monotonic and $q$-Bernstein functions.
In this paper, we provide some new generalizations of Feng Qi type integral inequalities on time scales by using elementary analytic methods.
In this short note we prove a conjecture for the interval $(0,1)$, related to a logarithmically completely monotonic function, presented in \cite{BG}. Then, we extend by proving a more generalized theorem. At the end we pose an open problem on a logarithmically completely monotonic function involving $q$-Digamma function.
It is defined $Γ_{p,q}$ function, a generalize of $Γ$ function. Also, we defined $ψ_{p,q}$-analogue of the psi function as the log derivative of $Γ_{p,q}$. For the $Γ_{p,q}$ -function, are given some properties related to convexity, log-convexity and completely monotonic function. Also, some properties of $ψ_{p,q} $ analog of the $ψ$ function have been established. As an application, when $p\to \infty, q\to 1,$ we obtain all result of \cite{Valmir1} and \cite{SHA}.
In the paper the authors alternatively prove that the function $x^α\big[\ln\frac{px}{x+p+1}-ψ_p(x)\big]$ is completely monotonic on $(0,\infty)$ if and only if $α\le 1$, where $p\in\mathbb{N}$ and $ψ_p(x)$ is the $p$-analogue of the classical psi function $ψ(x)$. This generalizes a known result.