Differential subordination for Janowski functions with positive real part

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."

Differential Subordinations For Functions With Positive Real Part Using Admissibility Conditions

“…Theorem 2.4. [7] Let the function p ∈ H [1, n] such that p(z) ≡ 1 and n ≥ 1 and Ω be a subset of C. The class Ψ n [Ω; A, B] is defined as the class of all those functions ψ :…”

“…In 2018, Madaan et al [23] established first and second order differential subordinations associated with the lemniscate of Bernoulli using admissibility technique. Further, Anand et al [7] also studied the generalized first order differential subordination for the Janowski functions. In 2019, Dorina Rȃducanu [30] established second order differential subordination implications associated with generalized Mittag-Leffler function.…”