Recently, Takahashi and Nunokawa (Appl. Math. Lett. 16:653-655, 2003) considered the class SS * (α, β) of analytic functions, which satisfy the condition -πβ/2 < arg{zf (z)/f (z)} < πα/2 for all z in the unit disc U on the complex plane, where 0 ≤ α < 1 and 0 ≤ β < 1. For α = β the class SS * (α, β) is equal to the well-known class SS * (β) of strongly starlike functions of order β. In this work, we derive a sufficient condition for analytic function to be in the class SS * (α, β). Our theorem is a generalization of the result of Nunokawa et al. (Bull. Inst. Math. Acad. Sin. 31(3):195-199, 2003). MSC: Primary 30C45
In this paper, we introduce and study a new one-parameter generalization of Pell numbers. We describe their distinct properties also related to matrix representation.
In this paper we investigate an interesting subclass BSðaÞ (0 a\1) of starlike functions in the unit disc D. The class BSðaÞ was introduced by Kargar et al. (Anal Math Phys, 2017. https://doi.org/10.1007/s13324-017-0187-3) which is strongly related to the Booth lemniscate. Some geometric properties of this class of analytic functions, including radius of starlikeness of order c (0 c\1), the image of f ðfz : jzj\rgÞ when f 2 BSðaÞ, an special example and estimate of bounds for Reff ðzÞ=zg, are studied.
Abstract. We investigate the family of functions f(z) = z + ^ anz n that are anan=2 lytic in the unit disk with the property that the domain of values f'(z) + zf"(z), (a g (-7r, 7r]) is the parabolic region (Imio) 2 < 2Rew -1. Integral representation and convolution characterization axe found and some coefficients bounds are given. Goodman investigated the class of uniformly convex functions UCV -a subclass of A consisting of functions convex in A and mapping circular arcs contained in the unit disk, with center at an arbitrary point in A, onto convex arcs. The class UCV has been later studied by R0nning [9] and Ma and Minda [6], [7]. IntroductionIn 1993 R0nning introduced the subclass of starlike functions Sp in the following way Sp = {F e S* : F(z) = zf'{z), f 6 UCV} .
In this paper we study some properties of functions f which are analytic and normalized (i.e. $$f(0)=0=f'(0)-1$$ f ( 0 ) = 0 = f ′ ( 0 ) - 1 ) such that satisfy the following subordination relation $$\begin{aligned} \left( \frac{zf'(z)}{f(z)}-1\right) \prec \frac{z}{(1-pz)(1-qz)}, \end{aligned}$$ z f ′ ( z ) f ( z ) - 1 ≺ z ( 1 - p z ) ( 1 - q z ) , where $$(p,q) \in [-1,1] \times [-1,1]$$ ( p , q ) ∈ [ - 1 , 1 ] × [ - 1 , 1 ] . These types of functions are starlike related to the generalized Koebe function. Some of the features are: radius of starlikeness of order $$\gamma \in [0,1)$$ γ ∈ [ 0 , 1 ) , image of $$f\left( \{z:|z|<r\}\right) $$ f { z : | z | < r } where $$r\in (0,1)$$ r ∈ ( 0 , 1 ) , radius of convexity, estimation of initial and logarithmic coefficients, and Fekete–Szegö problem.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.