Related papers: Some new inequalities for the gamma function
In this paper, we establish new general inequality for convex functions. Then we apply this inequality to obtain the midpoint, trapezoid and averaged midpoint-trapezoid integral inequality. Also, some applications for special means of real…
We study arithmetic inequalities for multiplicative, sub(super)-multiplicative, sub(super)-homogeneous functions. Applications for the classical arithmetic functions are pointed out.
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…
In this paper, we present the (p; q)-analogues of some inequalities concerning the digamma function. Our results generalize some earlier results.
Recently, the degenerate gamma functions are introduced as a degenerate version of the usual gamma function by Kim-Kim. In this paper, we investigate several properties of them. Namely, we obtain an analytic continuation as a meromorphic…
The main goal of this article is to present new types of inequalities refining and reversing inequalities of the harmonic mean of scalars and matrices. Furthermore, implementing the spectral decomposition of positive matrices, we present a…
This paper presents a family of new integral representations and asymptotic series of the multiple gamma function. The numerical schemes for high-precision computation of the Barnes gamma function and Glaisher's constant are also discussed.
We introduce a $p$-adic analogue of the incomplete gamma function. We also introduce quantities ($m$-values) associated to a function on natural numbers and prove a new characterization of $p$-adic continuity for functions with $p$-integral…
In this paper, we obtained some global approximation results for general Gamma type operators.
The Simes inequality has received considerable attention recently because of its close connection to some important multiple hypothesis testing procedures. We revisit in this article an old result on this inequality to clarify and…
In this paper, we establish several new inequalities for some differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Some applications for special means of real numbers are also provided.
This paper discusses the incomplete Gamma and Beta integrals involving the generalised hypergeometric function. The distribution of the largest and the smallest roots of a ratio arising in comparing the mean differences among groups is…
In this paper, we obtain some inequalities by using a kernel and an inequality which is a result of Young inequality. Besides we give some applications to special means.
In this paper, we give a new generalization of the Bohr inequality in refined form both for bounded analytic functions, and for sense-preserving harmonic functions with analytic part being bounded.
In this paper, we obtain some new inequalities for functions which are introduced by Godunova and Levin.
In the paper, the authors introduce a matrix-parametrized generalization of the multinomial probability mass function that involves a ratio of several multivariate gamma functions. They show the logarithmic complete monotonicity of this…
For $m,n\in \mathbb{N}$, let $0 < \alpha_i,\beta_j,\lambda_{ij} \leq 1$ be such that $\sum_{j=1}^n \lambda_{ij} = \alpha_i$, $\sum_{i=1}^m \lambda_{ij} = \beta_j$, and $\sum_{i=1}^m \alpha_i = \sum_{j=1}^n \beta_j \leq 1$. We prove that the…
Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind. In most cases, we show that we obtain the best possible constant or that our bounds are tight in certain limits. We…
In this paper, we obtain some new upper bounds for differantiable mappings whose q-th powers are geometrically convex and monotonically decreasing by using the H\"older inequality, Power mean inequality and properties of modulus.
In this paper, we prove logarithmically complete monotonicity properties of certain ratios of the $k$-gamma function. As a consequence, we deduce some inequalities involving the $k$-gamma and $k$-trigamma functions.