Differential Subordination and Coefficient Functionals of Univalent Functions Related to cos z

Differential subordination in the complex plane is the generalization of a differential inequality on the real line.  In this paper, we consider two subclasses of univalent functions associated with the trigonometric function coszcos⁡z. Using some properties of the hypergeometric functions, we determine the sharp estimate on the parameter ββ  such that the analytic function p(z)p(z) satisfying p(0)=1p(0)=1,  is subordinate to coszcos⁡z when the differential expression  p(z)+βz(dp(z)/dz)p(z)+βz(dp(z)/dz) is subordinate to the Janowski function. We compute sharp bounds on coefficient functional  Hermitian–Toeplitz determinants of the third and the fourth order with an invariance property for such functions. In addition, we estimate bound on Hankel determinants of the second and the third order.