FOURTH-ORDER DIFFERENTIAL SUBORDINATION RESULTS FOR ANALYTIC FUNCTIONS INVOLVING THE GENERALIZED BESSEL FUNCTIONS

FOURTH-ORDER DIFFERENTIAL SUBORDINATION RESULTS FOR ANALYTIC FUNCTIONS INVOLVING THE GENERALIZED BESSEL FUNCTIONS

S. Mandal , M. M. Soren

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Abstract

In this current paper, we obtain fourth-order differential subordination results for analytic functions in the open unit disk Δ = {z : z ∈ C and |z| < 1} associated with a new operator Sγ,k α,βf(z) which involves the generalized Bessel function of the 1st kind of order p and the Carlson-Shaffer operator. We also derive some interesting new results for this operator. The results are obtained by considering suitable classes of admissible functions.

Keywords

Admissible functions; Bessel functions; Carlson-Shaffer Operator; Fourthorder differential subordination; sandwich-type results.