Certain Coefficient Estimate Problems for Three-Leaf-Type Starlike Functions

Abstract

In our present investigation, some coefficient functionals for a subclass relating to starlike functions connected with three-leaf mappings were considered. Sharp coefficient estimates for the first four initial coefficients of the functions of this class are addressed. Furthermore, we obtain the Fekete–Szegö inequality, sharp upper bounds for second and third Hankel determinants, bounds for logarithmic coefficients, and third-order Hankel determinants for two-fold and three-fold symmetric functions.

Coefficient functionals for a class of bounded turning functions connected to three leaf function

“…Further, Babalola [2] studied the Hankel determinant H 3,1 (f) for some subclasses of analytic functions. For some current works on third order Hankel determinant we may mention (for example) [16,28,31]. The bound of the fourth Hankel determinant for a class of analytic functions with bounded turning associated with cardoid domain was approximated by Srivastava et al in [33].…”

“…and studied different geometric properties for this class. Further, Shi et al [28] investigated coefficient estimates problems for three leaf-type class. Now recall the definition of class R of bounded turning functions…”

A Subclass of Janowski Starlike Functions Involving Mathieu-Type Series

“…Motivated by a recently published article by Shi et al [30], in which they have found estimates for some coefficient functionals for three leaf-type starlike functions, from [31] where coefficient bounds for certain subclasses of analytic functions connected with Faber polynomial have been derived, and some other related works on this subject (see for example [32][33][34][35]). We will now define the following concepts:…”

Coefficient estimates for certain class of bi-univalent functions associated with κ-Fibonacci numbers

“…If f and g are two analytic functions in U, then f is subordinate to g, if there exists an analytic function w in U such that w(0) = 0 and |w(0)| < 1 for all z ∈ U that satisfies f = g o w in U. Symbolically, we write it as f ≺ g. If f ≺ g, then f (0) = g(0) and f (U) ⊆ g(U). A lot of the classes have studied in geometric function theory can be described in terms subordination (for details, see [5], [15], [16], [28], [29], [25]). Using subordination, Ma and Minda [35] gave a unified representation of various geometric subclasses of S such as S * α and K α which consisting of starlike and convex functions of order α (0 ≤ α < 1), respectively; which are usually characterized by the quantities zf (z)/f (z) or 1 + zf (z)/f (z) lying in a given domain in the right half-plane, for more details (see [21], [25]).…”