Subclasses of Analytic Functions Subordinated to the Four-Leaf Function

Abstract

The purpose of this research is to unify and extend the study of the well-known concept of coefficient estimates for some subclasses of analytic functions. We define the new subclass A4r,s of analytic functions related to the four-leaf domain, to increase the adaptability of our investigation. The initial findings are the bound estimates for the coefficients |an|, n=2,3,4,5, among which the bound of |a2| is sharp. Also, we include the sharp-function illustration. Additionally, we obtain the upper-bound estimate for the second Hankel determinant for this subclass as well as those for the Fekete–Szegő functional. Finally, for these subclasses, we provide an estimation of the Krushkal inequality for the function class A4r,s.

New Uses of q-Generalized Janowski Function in q-Bounded Turning Functions

“…The ϱth Hankel determinant of f (z), a concept presented by [34] can be defined when b ≥ 1 and ϱ ≥ 1: [5,[35][36][37]. Srivastava et al [5] recently characterized a fascinating class of bi-univalent functions incorporating Euler polynomials and determined the second Hankel determinant for this specific class.…”