Third-order differential sandwich-type results involving the Liu-Owa integral operator

Abstract

Some third-order differential subordination and superordination results are derived for multivalent analytic functions in the open unit disk, which are defined by using the Liu-Owa integral operator. In addition, we obtain new third-order differential sandwich-type results for this operator.

Results for Multivalent Functions Third-Order Differential Subordination and Superordination by Using New Differential Operator

“…When we talk about third-order differential subordination or superordination, we are specifically examining the relationships between the third derivatives of functions The concept of third-order differential subordination was recently introduced by Antonino and Miller (2), and Tang and Deniz have examined the outcomes (4), and You can see the results of third-order differential subordination in work for meromorphic function involving" Liu-Srivastava linear operator (5). (see, for instance, (3,6,7,8,9) on Third-order differential subordination and superordination drew the attention of several experts in this area. see, for instance (10,11,12).…”