In this paper, we introduce new concept that is fourth-order differential subordination and superordination associated with linear operator for univalent analytic functions in open unit disk. Here, we extended some lemmas. Also some interesting new results are obtained.
In this research, we study suitable classes of admissible functions and establish the properties of third-order differential subordination by making use a certain differential operator of analytic functions in U and have the normalized Taylor–Maclaurin series of the form: f(z)=z+∑n=2∞anzn, (z∈U). Some new results on differential subordination with some corollaries are obtained. These properties and results are symmetry to the properties of the differential superordination to form the sandwich theorems.
In this paper, by making use An operator, suitable classes of admissible functions are investigated and the properties of third-order differential subordination are obtained.
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