Second order non-linear strong differential subordinations

Abstract

The concept of differential subordination was introduced in [4] by S. S. Miller and P. T. Mocanu and the concept of strong differential subordination was introduced in [1] by J. A. Antonino and S. Romaguera. This last concept was applied in the special case of Briot-Bouquet strong differential subordination. In this paper we study the strong differential subordinations in the general case, following the general theory of differential subordinations presented in [4].

Strong differential subordination and superordination of analytic functions in connection with a linear operator

“…For the above two classes of admissible functions, G.I. Oros and G. Oros [13] proved the following result.…”

“…Definition 1.1. [13] Let φ : C 3 × U × U → C and let h(z) be univalent in U. If p(z) is analytic in U and satisfies the following (second-order) strong differential subordination:…”

“…In this present investigation, by making use of results of Oros and Oros [10,13], we consider certain suitable classes of admissible functions and investigate some strong differential subordination and strong differential superordination properties of analytic functions associated with the Kwon-Cho linear operator H λ ,q,s (α 1 ) defined by (1.6).…”

Strong differential sandwich results of l-pseudo-starlike functions with respect to symmetrical points

“…In recent years, several authors obtained many interesting results in strong differential subordination and superordination [1,3,4,11,12,13]. In this work, by making use of the strong differential subordination results and strong differential superordination results of Oros and Oros [8,9], we introduce and study certain suitable classes of admissible functions and derive some strong differential subordination and superordination properties of λpseudo-starlike functions with respect to symmetrical points.…”

On some differential sandwich theorems using an extended generalized S˘al˘agean operator and extended Ruscheweyh operator

“…Oros in [18]. Definition 1.1 [18] Let f (z, ζ), H (z, ζ) analytic in U × U . The function f (z, ζ) is said to be strongly subordinate to H (z, ζ) if there exists a function w analytic in U , with w (0) = 0 and |w (z)| < 1 such that f (z, ζ) = H (w (z) , ζ) for all ζ ∈ U .…”