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 ak+pz k+p (ak+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 f1(z) and f2(z) represented by ( f1∆ f2) (r, s; z) (r, s ∈ R) are(More)
The main object of this paper is to prove several inclusion relations associated with (j, δ)-neighborhoods of various subclasses defined by Salagean operator by making use of the familiar concept of neighborhoods of analytic functions. Special cases of some of these inclusion relations are shown to yield known results.
The purpose of the present article is to introduce several new subclasses 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 hypergeometric functions are also considered. 2000(More)
Abstract We introduce the subclass Tj(n, m, γ, α, λ) of analytic functions with negative coefficients defined by generalized Sălăgean operator D λ . Coefficient estimates, some important properties of the class Tj(n, m, γ, α, λ) and distortion theorems are determined. Further, extremal properties and radii of close-to-convexity, starlikeness and convexity(More)
By means of a certain extended fractional differintegral operator Ω (λ,p) z (−∞ < λ < p + 1; p ∈ N), the authors introduce and investigate two new subclasses of p-valently analytic functions of complex order. The various results obtained here for each of these function classes include coefficient inequalities and the consequent inclusion relationships(More)