No abstract

"Theory of differential subordination provides techniques to reduce differential subordination problems into verifying some simple algebraic condition called admissibility condition.We exploit the first order differential subordination theory to get several sufficient conditions for function satisfying several differential subordinations to be a Janowski function with positive real part. As applications, we obtain suffcient conditions for normalized analytic functions to be Janowski starlike functions."

No abstract

The main purpose of this investigation is to use quantum calculus approach and obtain the Bohr radius for the class of q-starlike (q-convex) functions of order α . The Bohr radius is also determined for a generalized class of q-Janowski starlike and q-Janowski convex functions with negative coefficients.

Let ϕ be a normalized convex function defined on open unit disk D . For a unified class of normalized analytic functions which satisfy the second order differential subordination f′(z) + αzf″(z) ≺ ϕ(z) for all z ∈ D , we investigate the distortion theorem and growth theorem. Further, the bounds on initial logarithmic coefficients, inverse coefficient and the second Hankel determinant involving the inverse coefficients are examined.