Abstract
In this current study, we aim to give some results for third-order differential subordination and superordination for analytic functions in U={z∈ℂ:|z|<1} involving the generalized operator Iα,βjf. The results are derived by investigating relevant classes of admissible functions. Some new results on differential subordination and superordination with some sandwich theorems are obtained. Moreover, several particular cases are also noted. The properties and results of the differential subordination are symmetry to the properties of the differential superordination to form the sandwich theorems.
Highlights
Indicate by H = H(U ) the collection of analytic functions in the open unit disc U that have the form: 2022, 14, 418. https://doi.org/10.3390/sym14020418Academic Editors: H[ a, n] =n f ∈ H(U ) : f (z) = a + an zn + an+1 zn+1 + an+2 zn+2 + · · ·Alexander Zaslavski, Ioan Ras, a,( a ∈ C, n ∈ N = {1, 2, 3, . . .}), Sergei D
A univalent function q is named a dominant of the solution of the differential subordination if p(z) ≺ q(z) for all p satisfying
The current paper utilizes the techniques on the third-order differential subordination and superordination outcomes of Antonino and Miller [7], Ali et al [18] and Tang et al [9], respectively and different conditions
Summary
A univalent function q is named a dominant of the solution of the differential subordination if p(z) ≺ q(z) for all p satisfying (2). An analytic function q is named subordinant of the solutions of the differential superordination, or more a subordinant if q(z) ≺ p(z) for all p satisfying (3). The current paper utilizes the techniques on the third-order differential subordination and superordination outcomes of Antonino and Miller [7], Ali et al [18] and Tang et al [9], respectively and different conditions (see [19,20]). Certain classes of admissible functions are investigated in this current paper, some properties of the third-order differential suborj dination and superordination for analytic functions in U related to the operator Iα,β f are mentioned
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