Related papers: Complete monotonicity of a function involving the …
Simple inequalities for some integrals involving the modified Bessel functions $I_{\nu}(x)$ and $K_{\nu}(x)$ are established. We also obtain a monotonicity result for $K_{\nu}(x)$ and a new lower bound, that involves gamma functions, for…
We consider convexity and monotonicity properties for some functions related to the $q$-gamma function. As applications, we give a variety of inequalities for the $q$-gamma function, the $q$-digamma function $\psi_q(x)$, and the $q$-series.…
We show that for any constant $c>0$, any (two-sided error) adaptive algorithm for testing monotonicity of Boolean functions must have query complexity $\Omega(n^{1/2-c})$. This improves the $\tilde\Omega(n^{1/3})$ lower bound of [CWX17] and…
Let $\alpha>0$ be a constant, let $\ell\ge0$ be an integer, and let $\Gamma(z)$ denote the classical Euler gamma function. With the help of the integral representation for the Riemann zeta function $\zeta(z)$, by virtue of a monotonicity…
We study the problem of invariance of indices of thematic factorizations. Such factorizations were introduced in [PY1] for studying superoptimal approximation by bounded analytic matrix functions. As shown in [PY1], the indices may depend…
In this paper the incomplete gamma function $\gamma(\alpha,x)$ and its derivative is considered for negative values of $\alpha $ and the incomplete gamma type function $\gamma_*(\alpha,x_-)$ is introduced. Further the polygamma functions…
We study the integral representation of $\Gamma$-limits of $p$-coercive integral functionals of the calculus of variations in the spirit of \cite{dalmaso-modica86}. We use infima of local Dirichlet problems to characterize the limit…
In this paper, we present a comprehensive study of the monotonicity and log-concavity of the generalized Marcum and Nuttall Q-functions. More precisely, a simple probabilistic method is firstly given to prove the monotonicity of these two…
For a broad class of integral functionals defined on the space of $n$-dimensional convex bodies, we establish necessary and sufficient conditions for monotonicity, and necessary conditions for the validity of a Brunn-Minkowski type…
A family of recently investigated Bernstein functions is revisited and those functions for which the derivatives are logarithmically completely monotonic are identified. This leads to the definition of a class of Bernstein functions, which…
If $\sigma$ is a symmetric mean and $f$ is an operator monotone function on $[0, \infty)$, then $$f(2(A^{-1}+B^{-1})^{-1})\le f(A\sigma B)\le f((A+B)/2).$$ Conversely, Ando and Hiai showed that if $f$ is a function that satisfies either one…
We derive local and global monotonic quantities associated to $p$-harmonic functions on manifolds with nonnegative scalar curvature. As applications, we obtain inequalities relating the mass of asymptotically flat $3$-manifolds, the…
In this paper our aim is to deduce some complete monotonicity properties and functional inequalities for the Bickley function. The key tools in our proofs are the classical integral inequalities, like Chebyshev, H\"older-Rogers,…
Necessary and sufficient conditions for a finite connected graph with a strict partial order on vertices to be a combinatorial invariant of pseudoharmonic function are obtained.
The paper studies logarithmic convexity and concavity of power series with coefficients involving q-gamma functions or q-shifted factorials with respect to a parameter contained in their arguments. The principal motivating examples of such…
We use the rationality of the generalized $h^{th}$ convergent functions, $Conv_h(\alpha, R; z)$, to the infinite J-fraction expansions enumerating the generalized factorial product sequences, $p_n(\alpha, R) =…
We consider positive solutions to $\displaystyle -\Delta_p u=\frac{1}{u^\gamma}+f(u)$ under zero Dirichlet condition in the half space. Exploiting a prio-ri estimates and the moving plane technique, we prove that any solution is monotone…
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.
We characterize real functions $f$ on an interval $(-\alpha,\alpha)$ for which the entrywise matrix function $[a_{ij}] \mapsto [f(a_{ij})]$ is positive, monotone and convex, respectively, in the positive semidefiniteness order. Fractional…
Let $X=\{X_n: n\in\mathbb{N}\}$ be a long memory linear process in which the coefficients are regularly varying and innovations are independent and identically distributed and belong to the domain of attraction of an $\alpha$-stable law…