In this paper, we familiarize a class of multivalent functions with respect to symmetric points related the differential operator and discuss impact Janowski on conic regions. Inclusion results, subordination property, coefficient inequalities are obtained. Further, applications our results that extensions those given in earlier works presented as corollaries.

Both the theory of differential subordination and its dual, superordination, introduced by Professors Miller Mocanu are based on reinterpreting certain inequalities for real-valued functions case complex-valued functions. Studying superordination properties using different types operators is a technique that still widely used, some studies resulting in sandwich-type theorems as present paper. T...

In [4], under some easy to remove genericity assumptions, we proved the analytic subordination of the Cauchy transforms of distributions GμX+Y and GμX for a pair of freely independent self-adjoint random variables X, Y . We used this to obtain inequalities among p-norms of densities of distributions, free entropies and Riesz energies. This was followed by P.Biane’s discovery [1] that subordinat...