In his 1984 proof of the Bieberbach and Milin conjectures de Branges used a positivity result of special functions which follows from an identity about Jacobi polynomial sums that was found by Askey and Gasper in 1973, published in 1976. In 1991 Weinstein presented another proof of the Bieberbach and Milin conjectures, also using a special function system which (by Todorov and Wilf) was realize...

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 ...

Conflict processing is assumed to serve two crucial, yet distinct functions: Regarding task performance, control is adjusted to overcome the conflict. Regarding task choice, control is harnessed to bias decision making away from the source of conflict. Despite recent theoretical progress, until now two lines of research addressed these conflict-management strategies independently of each other....

This article defines a new operator called the q-Babalola convolution by using quantum calculus and of normalized analytic functions in open unit disk. We then study class bi-univalent defined disk associated with operator. The main results investigation include some upper bounds for initial Taylor–Maclaurin coefficients Fekete–Szego inequalities class. Many applications finds are highlighted c...

In numerous geometric and physical applications of complex analysis, estimating the sharp bounds coefficient-related problems univalent functions is very important due to fact that these coefficients describe core inherent properties conformal maps. The primary goal this paper was calculate estimates initial some their combinations (the Hankel determinants, Zalcman’s functional, etc.) for class...

Recently the present authors established refined versions of Bohr's inequality in case bounded analytic functions. In this article, we state and prove a generalization these results. Here, consider image origin boundary unit disk under function question let distance between both play central role our theorems. Thereby extend Bohr for class quasi-subordinations which contains classes majorizatio...

and Applied Analysis 3 The equation satisfied by the free boundary is 4, 6 Re [ Ḟ ζ, t ζF ′ ζ, t ] Q 2π , ζ e 1.5 for the zero tension surface model and Re [ Ḟ ζ, t ζF ′ ζ, t ] Q 2π − γH [ i ∂k ∂t ( e, t )] θ , ζ e 1.6 for the small surface tension model. 2. The Inner Problem (Bounded Domains) In this section, we obtain the invariance in time ofΦ-likeness property for the inner problem. Startin...

The Bieberbach conjecture about the coefficients of univalent functions of the unit disk was formulated by Ludwig Bieberbach in 1916 [4]. The conjecture states that the coefficients of univalent functions are majorized by those of the Koebe function which maps the unit disk onto a radially slit plane. The Bieberbach conjecture was quite a difficult problem, and it was surprisingly proved by Lou...