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

Pratima Rai; Sushil Kumar

doi:10.52737/18291163-2026.16.09-1-18

Authors

Pratima Rai University of Delhi
Sushil Kumar Bharati Vidyapeeth's College of Engineering

DOI:

https://doi.org/10.52737/18291163-2026.16.09-1-18

Keywords:

Differential Subordination, Univalent Functions, Starlike Functions, Convex Function, cos z, Hermitian-Toeplitz Determinant, Hankel Determinant

Abstract

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 $\cos z$. Using some properties of the hypergeometric functions, we determine the sharp estimate on the parameter $\beta$ such that the analytic function $p(z)$ satisfying $p(0)=1$, is subordinate to $\cos z$ when the differential expression $p(z)+\beta z (dp(z)/dz)$ 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.

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