Preserving subordination and superordination results of generalized Srivastava-Attiya operator

Abstract

and let A (1) = A. For f ,F ∈ H(U), the function f(z) is said to be subordinate to F (z), or F (z) is superordinate to f(z), if there exists a function ω(z) analytic in U with ω(0) = 0 and |ω(z)| < 1(z ∈ U), such that f(z) = F (ω(z)). In such a case we write f(z) ≺ F (z). If F is univalent, then f(z) ≺ F (z) if and only if f(0) = F (0) and f(U) ⊂ F (U) (see [14] and [15]). Let φ : C×U → C and h (z) be univalent in U. If p (z) is analytic in U and satisfies the first order differential subordination: