Let f and F be members of . The function f is said to be subordinate to F, or F is said to be superordinate to f , if there exists a function w analytic in U, with w(0)= 0 and |w(z)| < 1, and such that f (z)= F(w(z)). In such a case, we write f ≺ F or f (z)≺ F(z). If the function F is univalent in U, then f ≺ F if and only if f (0)= F(0) and f (U)⊂ F(U) (cf. [1, 2]). Let φ : C2 → C and let h be...

In this research, we develop some differential subordination results involving harmonic means of $f_{b}(z),f_{b}(z)+zf_{b}^{\prime}(z)$ and $f_{b}(z)+\frac{zf_{b}^{\prime}(z)}{f_{b}(z)},$ where $f_{b}(z)=\frac{z}{\left(1-z^{n}\right) ^{b}},$ $b\geq0;n\in\mathbb{N}=1,2,3...$ is an $n$-fold symmetric Koebe type functions defined in the unit disk with $f_{b}(0)=0,f_{b}^{\prime}(z)\neq0.$ By using ...

The results obtained by the authors in present article refer to quantum calculus applications regarding theories of strong differential subordination and superordination. q-analogue multiplier transformation is extended, order be applied on specific classes functions involved superordination theories. Using this extended transformation, a new class analytic normalized introduced investigated. c...

In this paper we introduce a certain general class Φp (a, c, A,B) (β ≥ 0, a > 0, c > 0, −1 ≤ B < A ≤ 1, p ∈ N = {1, 2, ...}) of multivalent analytic functions in the open unit disc U = {z : |z| < 1} involving the linear operator Lp(a, c). The aim of the present paper is to investigate various properties and characteristics of this class by using the techniques of Briot-Bouquet differential subo...