Work

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

Year: 2024

Type: article

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.

Source: Armenian Journal of Mathematics

DOI: 10.52737/18291163-2026.16.09-1-18

Authors: Pratima Rai, Sushil Kumar

Institutions: University of Delhi, Bharati Vidyapeeth's College of Engineering, Delhi, Bharati Vidyapeeth (Deemed to be University)

Language: English

Topic: Analytic and geometric function theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: University of Delhi

Awards: G1033897659, G5908233825, G7790377078