We introduce the subclass P P j, , β£ , n of starlike functions with negative coefficients by using the differential operator D n which was considered by G. S ΒΈt.
Generalizations of Hadamard Products of Functions with Negative Coefficients
β Scribed by Jae Ho Choi; Yong Chan Kim; Shigeyoshi Owa
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 113 KB
- Volume
- 199
- Category
- Article
- ISSN
- 0022-247X
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β¦ Synopsis
Let T T n be the class of functions with negative coefficients which are analytic Ε½ . Ε½ . Ε½ . in the unit disk U U. For functions f z and f z belonging to T T n , generaliza-1 2 Ε½ . Ε½ . Ε½ .Ε½ . tions of the Hadamard product of f z and f z represented by f ^f p,q; z 1 2 1 2 are introduced. In the present paper, some interesting properties of these generali-Ε½ . Ε½ . zations of Hadamard products of functions in T T * n, β£ and C C n, β£ are given.
π SIMILAR VOLUMES
A function q ( z ) is said to be convex if it is a univalent conformal mapping of the unit disk 1x1 -= 1, hereafter called U , onto a convex domain. The HADAMARD product or convolution of two power series f ( 2 ) : = anzn and g(x) : = b,znis defined as the power series (f\*g) ( x ) : = anb,xn. The f
The authors introduce and study three novel subclasses of analytic and p-valent functions with negative coefficients. In addition to finding a necessary and sufficient condition for a function to belong to each of these subclasses, a number of other potentially useful properties and characteristics
The aim of this paper is to give a bivariate asymptotic expansion of the coefficient \(y_{n k}=\left[x^{n}\right] y(x)^{k}\), where \(y(x)=\sum y_{n} x^{n}\) has a power series expansion with non-negative coefficients \(y_{n} \geqslant 0\). Such expansions are known for \(k / n \in[a, b]\) with \(a>