Fifth Coefficient Estimate for Certain Starlike Functions

Abstract

Let λ ∈ [0, 1] and p ∈ N, we introducewhere ϕ is a Ma-Minda function. We obtain sharp bound for a particular case of the generalized Zalcman conjecture and for some combinations involving the initial coefficients of f in S * λ,p (ϕ). Further sharp estimate for the fifth coefficient of functions belonging to S * 0,1 (ϕ) =: S * (ϕ) is deduced. Applications appear for several well-known classes for the particular choices of λ, p and ϕ(z) along with a dominance result for the class S * (ϕ).

Radius and Convolution problems of analytic functions involving Semigroup Generators

“…Subclasses of S * are studied for various choices of ϕ. For these subclasses, we refer [8,14]. Kumar and Gangania [15] introduced and studied the class…”

Hermitian-Toeplitz determinants for certain univalent functions

“…Various subclasses of S * and C are considered for different choices of ϕ(z) [6,14]. For other subclasses and their corresponding class notation see [5,Table 1]. We use these notations directly in the results.…”