Argument and Coefficient Estimates for Certain Analytic Functions

Abstract

The aim of the present paper is to introduce a new class G α , δ of analytic functions in the open unit disk and to study some properties associated with strong starlikeness and close-to-convexity for the class G α , δ . We also consider sharp bounds of logarithmic coefficients and Fekete-Szegö functionals belonging to the class G α , δ . Moreover, we provide some topics related to the results reported here that are relevant to outcomes presented in earlier research.

Logarithmic Coefficient Bounds and Coefficient Conjectures for Classes Associated with Convex Functions

“…where Hðq 1 ; q 2 Þ is given in ([26], Lemma 2) (or [9], Lemma 5), q 1 = ðB 1 + ð4B 2 /B 1 ÞÞ/2, and q 2 = ðB 2 + ð2B 3 /B 1 ÞÞ/2. The bounds (20) and ( 21) are sharp.…”

“…For example, taking φðzÞ = ð1 + AzÞ/ð1 + BzÞ where A ∈ ℂ, −1 ≤ B ≤ 0, and A ≠ B, we get the classes S * ½A, B and C½ A, B, respectively (see also [9,10]). The mentioned classes with the restriction −1 ≤ B < A ≤ 1 reduce to the popular Janowski starlike and Janowski convex functions, respectively.…”

“…play as extremal functions for some issues of the families ST hpl ðsÞ and CV hpl ðsÞ, respectively. Lately, several researchers have subsequently investigated same problems regarding the logarithmic coefficients and the coefficient problems [9,[13][14][15][16][17][18][19][20][21][22][23], to mention a few of them. For instance, the rotation of the Koebe function kðzÞ = z ð1 − e iθ zÞ −2 for each θ ∈ ℝ has the logarithmic coefficients…”

Properties of a Class of Analytic Functions Influenced by Multiplicative Calculus

“…Belonging to R m k, λ (α, β, γ; ψ) Inspired by recent works like [36][37][38], in this section we determine the coefficient bounds and Fekete-Szegő problem associated with the logarithmic function.…”

New Results for Some Generalizations of Starlike and Convex Functions

“…where q 1 = ðL 1 + ð4L 2 /L 1 ÞÞ/2, q 2 = ðL 2 + ð2L 3 /L 1 ÞÞ/2 and K ðq 1 ; q 2 Þ is given by (see [17,18])…”