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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)
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.
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)