Abstract
Problem statement: The object of this study is to obtain certain differential subordinations. Approach: Here we use known generalized differential operator given by Darus and Ibrahim and well known lemmas given by Miller and Mocanu. Results: We will pose several results on subordination theorems. Conclusion: Many other results can be obtained by using the operator defined.
Highlights
Let H be the class of analytic functions in U := {z ∈ C :| z |< 1} and H[a,n] be the subclass of H consisting of functions of the form f (z) = a + a n zn + an+1zn+1 +
Let φ : C2 → C and let h be univalent in UIf p is analytic in U and satisfies the differential subordination φ(p(z)),zp′(z)) ≺ h(z) p is called a solution of the differential subordination
The univalent function q is called a dominant of the solutions of the differential subordination, p ≺ q
Summary
. Let A be the subclass of H consisting of functions of the form Eq 1: f (z) = z + ∑∞ anzn Let φ : C2 → C and let h be univalent in UIf p is analytic in U and satisfies the differential subordination φ(p(z)),zp′(z)) ≺ h(z) p is called a solution of the differential subordination. The univalent function q is called a dominant of the solutions of the differential subordination, p ≺ q.
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