In this paper, we introduce the concept of ternary antiderivation on Banach algebras and investigate stability in algebras, associated to $(\alpha,\beta)$-functional inequality: \begin{align*} &\Vert \mathcal{F}(x+y+z)-\mathcal{F}(x+z)-\mathcal{F}(y-x+z)-\mathcal{F}(x-z)\Vert \nonumber\\ &\leq \Vert \alpha (\mathcal{F}(x+y-z)+\mathcal{F}(x-z)-\mathcal{F}(y))\Vert + \beta (\mathcal{F}(x-...

For a sequence \begin{document}$ (a_n) $\end{document} of complex numbers we consider the cubic parabolic polynomials f_n(z) = z^3+a_n z^2+z and (F_n) iterates F_n f_n\circ\dots\circ f_1 . The Fatou set \mathcal{F}_0 is all z\in\hat{\mathbb{C}} such that normal. complement called Julia denoted by \mathcal{J}_0 aim this paper to study some properties As particular case, when constant, a_n , then...

In this paper, we mainly announce the result: every Siegel-Hilbert cuspform of weight divisible by 4h and of square-free level relative to certain congruence subgroups is a linear combination of theta series. I N T R O D U C T I O N Theta series provides one of the two most explicit ways to construct holomorphic modular forms. The other way is by Eisenstein series. A virtue of theta series is t...

Let S stand for the usual class of univalent regular functions in the unit disk U = {z : |z| < 1} normalized by f(z) = z + a2z + . . . in U , and let S be its subclass defined by restricting |f(z)| < M in U , M ≥ 1. We consider two classical problems: Bombieri’s coefficient problem for the class S and the sharp estimate of the fourth coefficient of a function from S . Using Löwner’s parametric ...

The name comes from elementary geometry: if a right triangle has leg lengths x and y and hypotenuse length z, then x + y = z. Of course here x, y, z are positive real numbers. For most integer values of x and y, the integer x + y will not be a perfect square, so the positive real number √ x2 + y2 will be irrational: e.g. x = y = 1 =⇒ z = √ 2. However, a few integer solutions to x + y = z are fa...

PURPOSE The purpose was to determine the number of semantic neighbors, namely, semantic set size, for 88 nonobjects (J. F. Kroll & M. C. Potter, 1984) and determine how semantic set size related to other measures and age. METHOD Data were collected from 82 adults and 92 preschool children in a discrete association task. The nonobjects were presented via computer, and participants reported the...

In the present article we observe the significations and the dimensions of interaction between instruments and performers in musical performance. This will lead us, firstly, to consider interaction as a phenomenon non-exclusively correlated with the use of numeric technologies. Then, still within the realm of interaction, we describe some of the transmutations introduced by digital music instru...