Radius Problems for Some Subclasses of Analytic Functions

In this paper, we consider a subclass of starlike functions associated with a vertical strip domain. Several results concerned with integral representations, convolutions, and coefficient inequalities for functions belonging to this class are obtained. Furthermore, we consider radius problems and inclusion relations involving certain classes of strongly starlike functions, parabolic starlike functions and other types of starlike functions. The results are essential improvements of the corresponding results obtained by Kargar et al., and the derivations are similar to those used earlier by Sun et al. and Kwon et al..2010 Mathematics Subject Classification. Primary 30C45; Secondary 30C55.

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“…Recently, Kargar et al [2] introduced the analytic function F α and the vertical strip Ω α , which are defined as follows:…”

Section: Preliminariesmentioning

confidence: 99%

“…In a recent paper, Kargar et al [2] investigated the class MS(α) defined below, and obtained several radius results for certain well-known function classes. Definition 1.…”

Section: Introductionmentioning

confidence: 99%

On a subclass of starlike functions associated with a vertical strip domain

et al. 2019

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“…for some 0 ≤ α < 1 and β > 1. Also, they (see [5]) introduced the class M(δ) including all functions f ∈ A such that…”

Section: Introductionmentioning

confidence: 99%

A new subclass of analytic functions

Sokół

Mahzon

2020

Hacettepe Journal of Mathematics and Statistics

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In the present paper, we introduce a class B θ (α, β) of functions, analytic in |z| < 1, such that f (0) = 0, f (0) = 1 andwhere θ ∈ (−π, π], 0 ≤ α < 1 and β > 1. Integral representation, differential subordination results and coefficient estimates are considered. Also Fekete-Szegö coefficient functional associated with the k-th root transform [f (z k )] 1/k for functions in the class B θ (α, β) is investigated.Mathematics Subject Classification (2010). 30C45; 30C50

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“…Several authors considered various special cases of the class of Janowski starlike functions by considering some specific functions, namely ϕ q (z) := z + √ 1 + z 2 , ϕ 0 (z) := 1 + (z/k)((k + z)/(k − z)) (k = √ 2 + 1) , ϕ s (z) := 1 + sin z, and G α (z) := 1 + z/(1 − αz 2 ). Some of those classes are: S * L := S * ( √ 1 + z) [4], S * q := S * (ϕ q (z)) [5], S * e = S * (e z ) [6], S * R = S * (ϕ 0 ) [7], S * s = S * (ϕ s ) [8]) , BS * (α) := S * (G α (z)), 0 ≤ α < 1 [9,10]. For a brief survey on these classes, readers may refer to [11,12].…”

Section: Introductionmentioning

confidence: 99%