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Let T (n, p) denote the class of functions of the form f (z) = z p − ∞ k=n a k+ p z k+ p (a k+ p ≥ 0; p, n ∈ N) which are analytic and p-valent in the open unit disc U = {z : |z| < 1}. For functions f j (z) (j = 1, 2) belonging to T (n, p), generalizations of the modified-Hadamard product of f 1 (z) and f 2 (z) represented by (f 1 ∆ f 2) (r, s; z) (r, s ∈… (More)

Let J n (α) denote the classes of functions of the form f (z) = 1 z + ∞ k=0 a k z k , which are regular in the punctured disc U * = {z : 0 < |z| < 1} and satisfy Re (D n+1 f (z)) (D n f (z)) − 2 < − n + α n + 1 , z ∈ U * , n ∈ N = {0, 1, ...} and α ∈ [0, 1), where D n f (z) = 1 z z n+1 f (z) n! (n). In this paper it is proved that J n+1 (α) ⊂ J n (α) (n ∈ N… (More)

A new class of analytic functions of complex order is defined using a generalized differential operator. Coefficient inequalities, sufficient condition and an interesting subordination result are obtained. [1] F. M. AL-OBOUDI, On univalent functions defined by a generalized S˘ al˘ agean operator, Int.

- H. E. Darwish
- 2008

Using of Salagean operator, we define a new subclass of uniformly convex functions with negative coefficients and with fixed second coefficient. The main objective of this paper is to obtain coefficient estimates, distortion bounds, closure theorems and extreme points for functions belonging of this new class. The results are generalized to families with… (More)

- H. E. Darwish
- 2011

The purpose of the present article is to introduce several new sub-classes of meromorphic functions defined by using the multiplier transformation and hypergeometric function and investigate various inclusion relationships for these subclasses. Some interesting applications involving a certain class of hypergeomet-ric functions are also considered.

- H. E. Darwish
- 2008

We introduce the subclass T j (n, m, γ, α, λ) of analytic functions with negative coefficients defined by generalized S˘ al˘ agean operator D n λ. Coefficient estimates, some important properties of the class T j (n, m, γ, α, λ) and distortion theorems are determined. Further, extremal properties and radii of close-to-convexity, starlikeness and convexity… (More)