H. E. Darwish

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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.
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.
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)