Using the Bernstein theorem we give a simple proof of complete monotonicity three parameter generalized Mittag-Leffler function $E_{\alpha, \beta}^{\gamma}(-x)$ for $x \geq 0$ and suitably adjusted parameters $\alpha$, $\beta$ $\gamma$

background: thalassemia is one of the most common hereditary disorders and beta-thalassemia major is its severe form. the present study is concerned with the analysis of liver function, thyroid function and estimation of critical serum ions as well as hematological characteristics in beta-thalassemia patients and controls. subjects and methods: the study included 54 patients with beta-thalassem...

Let $E$ be the self-similar set generated by {\it iterated function system} {\[ f_0(x)=\frac{x}{\beta},\quad f_1(x)=\frac{x+1}{\beta}, \quad f_{\beta+1}=\frac{x+\beta+1}{\beta} \]}with $\beta\ge 3$. {Then} is a with complete {overlaps}, i.e., $f_{0}\circ f_{\beta+1}=f_{1}\circ f_1$, but not totally self-similar. We investigate all its generating systems, give spectrum of $E$, and determine Haus...

We introduce the concept of generalized \(\beta\) - \(\gamma\) Z contraction mapping with respect to a simulation function ξ and study existence fixed points for such mappings in complete -metric spaces. Further, we extend it partially ordered

In the paper, authors establish an inequality involving exponential functions and sums, introduce a ratio of finitely many gamma functions, discuss properties, including monotonicity, logarithmic convexity, (logarithmically) complete Bernstein function property, newly introduced ratio, construct two inequalities multinomial coefficients multivariate beta functions.

In the paper, by virtue of convolution theorem for Laplace transforms and analytic techniques, author finds necessary sufficient conditions complete monotonicity, inequalities several functions involving polygamma functions. By these results, derives a lower bound function related to sectional curvature Fisher–Rao manifold beta distributions.

Let$mathbb{C}^n$ be the space of $n$ complex variables. Let$Omega_{n,p_2,ldots,p_n}$ be a complete Reinhardt on$mathbb{C}^n$. The Minkowski functional on complete Reinhardt$Omega_{n,p_2,ldots,p_n}$ is denoted by $rho(z)$. The concept ofspirallike mapping of type $beta$ and order $alpha$ is defined.So, the concept of the strong and almost spirallike mappings o...