On Analytic Multivalent Function Associated with Cosine Hyperbolic Function

Abstract

In this article, we set up some adequate conditions for analytic functions associated with cosine hyperbolic function. We determine conditions on α such that
 1+α (ϰ^(2+P(j-1) ) g^' (ϰ))/(Pg^j (ϰ)),for each j=0,1,2,3
 are subordinated by Janowski function, then (g(ϰ))/ϰ^P <cosℏ⁡(ϰ),(ϰ∈C). By choosing specific values of functions g we get some adequate conditions for multivalent starlike function related with cosine hyperbolic.