Some classes of analytic functions involving Noor integral operator

Abstract

The object of the present paper is to investigate some inclusion properties of certain subclasses of analytic functions defined by using the Noor integral operator. The integral preserving properties in connection with the operator are also considered. Relevant connections of the results presented here with those obtained in earlier works are pointed out.  2005 Elsevier Inc. All rights reserved.

Some subclasses of analytic functions involving the generalized Noor integral operator

“…(i) Setting n = λ = 1, c = b, a = k + p in Theorem 3.23 and Corollary 3.24, we obtain Theorem 3.3 and Corollary 3.4 in [18]. (ii) Setting p = 1, n = λ = 1, c = b, a = k + p in Theorem 3.23, we obtain Corollary 2.2 in [4].…”

“…The operator I λ p,1 (a, 1; c) was introduced recently by Cho et al [5] and I 1 p,1 (n + p, c; c) was introduced by Patel and Cho [18]. For convenience, we write I λ p,n (a, b; c)f (z) = I λ p,n (a, b; c).…”

“…In particular, we denote S λ p,n (a, b, c; β; 1, −1) by S λ p,n (a, b, c; β). Furthermore, S 1 1,1 (k + p, c, c; β; A, B) is the class introduced and studied by Cho [4]; S 1 p,1 (k + p, c, c; β; A, B) is the class introduced and studied by Patel and Cho [18].…”

On sandwich theorems for higher-order derivatives of multivalent analytic functions associated with the generalized Noor integral operator

“…(i) I 1 p,1 (k + p, c, c) = I k,p (n∈ N) the operator introduced by Liu and Noor [16] and Patel and Cho [21]. (ii) I λ p,1 (a, 1, c) = I λ p (a, c) the operator considered by Cho et al [8].…”

Differential sandwich theorems for multivalent functions

“…The operator D λ+p−1 f : A p −→ A p was introduced by Patel and Cho [12]. In particular, D λ f : A → A for p = 1 and λ ≥ −1 was introduced by Ruschweyh [14].…”