Some generalizations of the Eneström–Kakeya theorem

Let p(z) = a0 + a1z + a2z2 + ... + anzn be a polynomial of degree n; where the coefficients aj, j = 0, 1, 2, ..., n, are real numbers. We impose some restriction on the coefficients and then prove some extensions and generalizations of the Eneström–Kakeya theorem

Generalized weighted Ostrowski and Ostrowski-Gruss type inequalities on time scales via a parameter function

We prove generalized weighted Ostrowski and Ostrowski–Gr ¨uss type inequalities on time scales via a parameter function. In particular, our result extends a result of Dragomir and Barnett. Furthermore, we apply our results to the continuous, discrete, and quantum cases, to obtain some interesting new inequalitie

Time Scale Inequalities of the Ostrowski Type for Functions Differentiable on the Coordinates

In 2016, some inequalities of the Ostrowski type for functions (of two variables) differentiable on the coordinates were established. In this paper, we extend these results to an arbitrary time scale by means of a parameter λ∈0,1. The aforementioned results are regained for the case when the time scale T=R. Besides extension, our results are employed to the continuous and discrete calculus to get some new inequalities in this direction

Annular Regions Containing All the Zeros of a Polynomial via Special Numbers

In this paper, we obtain some results concerning annular regions containing all the zeros of a given polynomial. These annular regions have radii in terms of the Bell numbers, Pell numbers, Stirling numbers, Fibonacci numbers, Motzkin numbers, Catalan numbers, and/or the Schr¨oder numbers. Also, we show, by means of examples, that for some polynomials our results sharpen some of the known results in this direction

A new weighted Ostrowski type inequality on arbitrary time scale

In this paper, we prove a new weighted generalized Montgomery identity and then use it to obtain a weighted Ostrowski type inequality for parameter function on an arbitrary time scale. In addition, the real, discrete and quantum cases are considered