scholarly journals Starlike Functions Related to the Bell Numbers

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 219 ◽  
Author(s):  
Nak Cho ◽  
Sushil Kumar ◽  
Virendra Kumar ◽  
V. Ravichandran ◽  
H. Srivastava
Keyword(s):  
Starlike Functions ◽  
Differential Subordination ◽  
Positive Real Part ◽  
Bell Numbers ◽  
Positive Real ◽  
First Order

The present paper aims to establish the first order differential subordination relations between functions with a positive real part and starlike functions related to the Bell numbers. In addition, several sharp radii estimates for functions in the class of starlike functions associated with the Bell numbers are determined.

scholarly journals Differential subordination for Janowski functions with positive real part

2021 ◽  
Vol 66 (3) ◽  
pp. 457-470
Author(s):  
Swati Anand ◽  
V. Ravichandran ◽  
Sushil Kumar
Keyword(s):  
Sufficient Conditions ◽  
Starlike Functions ◽  
Differential Subordination ◽  
Positive Real Part ◽  
Algebraic Condition ◽  
Positive Real ◽  
First Order ◽  
Janowski Functions ◽  
Subordination Theory ◽  
Differential Subordinations

"Theory of differential subordination provides techniques to reduce differential subordination problems into verifying some simple algebraic condition called admissibility condition.We exploit the first order differential subordination theory to get several sufficient conditions for function satisfying several differential subordinations to be a Janowski function with positive real part. As applications, we obtain suffcient conditions for normalized analytic functions to be Janowski starlike functions."

Sharp coefficient bounds for starlike functions associated with the Bell numbers

2019 ◽  
Vol 69 (5) ◽  
pp. 1053-1064 ◽  
Author(s):  
Virendra Kumar ◽  
Nak Eun Cho ◽  
V. Ravichandran ◽  
H. M. Srivastava
Keyword(s):  
Starlike Functions ◽  
Higher Order ◽  
Positive Real Part ◽  
Bell Numbers ◽  
Positive Real ◽  
Sharp Bounds ◽  
Hankel Determinants ◽  
Coefficient Bounds ◽  
The Family ◽  
Schwarzian Derivatives

Abstract Let $\begin{array}{} \mathcal{S}^*_B \end{array}$ be the class of normalized starlike functions associated with a function related to the Bell numbers. By establishing bounds on some coefficient functionals for the family of functions with positive real part, we derive for functions in the class $\begin{array}{} \mathcal{S}^*_B \end{array}$ several sharp coefficient bounds on the first six coefficients and also further sharp bounds on the corresponding Hankel determinants. Bounds on the first three consecutive higher-order Schwarzian derivatives for functions in the class $\begin{array}{} \mathcal{S}^*_B \end{array}$ are investigated.

scholarly journals Applications of first order differential subordination for functions with positive real part

2018 ◽  
Vol 63 (3) ◽  
pp. 303-311 ◽  
Author(s):  
Om P. Ahuja ◽  
◽  
Sushil Kumar ◽  
V. Ravichandran ◽  
◽  
...  
Keyword(s):  
Differential Subordination ◽  
Positive Real Part ◽  
Positive Real ◽  
First Order

scholarly journals Disk-like functions

1970 ◽  
Vol 11 (2) ◽  
pp. 251-256
Author(s):  
Richard J. Libera
Keyword(s):  
Unit Disk ◽  
Geometric Property ◽  
Starlike Functions ◽  
Positive Real Part ◽  
Open Unit ◽  
Open Unit Disk ◽  
Positive Real ◽  
Image Position

The class s of functions f(z) which are regular and univalent in the open unit disk △ = {z: |z| < 1} each normalized by the conditionshas been studied intensively for over fifty years. A large and very successful portion of this work has dealt with subclasses of L characterized by some geometric property of f[Δ], the image of Δ under f(z), which is expressible in analytic terms. The class of starlike functions in L is one of these [3]; f(z) is starlike with respect to the origin if the segment [0,f(z)] is in f[Δ] for every z in Δ and this condition is equivalent to requiring that have a positive real part in Δ.

scholarly journals Differential inequalities for spirallike and strongly starlike functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nak Eun Cho ◽  
Oh Sang Kwon ◽  
Young Jae Sim
Keyword(s):  
Analytic Function ◽  
Sufficient Conditions ◽  
Starlike Functions ◽  
Differential Subordination ◽  
Differential Inequalities ◽  
First Order ◽  
Strongly Starlike Functions ◽  
Strongly Starlike ◽  
Spirallike Functions

AbstractIn this paper, by using a technique of the first-order differential subordination, we find several sufficient conditions for an analytic function p such that $p(0)=1$ p ( 0 ) = 1 to satisfy $\operatorname{Re}\{ {\mathrm{e}}^{{\mathrm{i}}\beta } p(z) \} > \gamma $ Re { e i β p ( z ) } > γ or $| \arg \{p(z)-\gamma \} |<\delta $ | arg { p ( z ) − γ } | < δ for all $z\in \mathbb{D}$ z ∈ D , where $\beta \in (-\pi /2,\pi /2)$ β ∈ ( − π / 2 , π / 2 ) , $\gamma \in [0,\cos \beta )$ γ ∈ [ 0 , cos β ) , $\delta \in (0,1]$ δ ∈ ( 0 , 1 ] and $\mathbb{D}:=\{z\in \mathbb{C}:|z|<1 \}$ D : = { z ∈ C : | z | < 1 } . The results obtained here will be applied to find some conditions for spirallike functions and strongly starlike functions in $\mathbb{D}$ D .

scholarly journals Subordination of functions in subclass of Bazilevič Functions B 1(α, β)

2021 ◽  
Vol 2106 (1) ◽  
pp. 012026
Author(s):  
Marjono
Keyword(s):  
Unit Disc ◽  
Starlike Functions ◽  
Positive Real Part ◽  
Positive Real ◽  
Sharp Estimates ◽  
Strongly Starlike Functions ◽  
Strongly Starlike ◽  
Coefficient Problems ◽  
Bazilevic Functions

Abstract Let f be analytic in the unit disc D = {z : |z| < 1} with f ( z ) = z + ∑ n = 2 ∞ a n z n , and for α ≥ 0 and 0 < β ≤ 1, let B 1(α, ß), denote for the class of Bazilevič functions satisfying the expression | arg z 1 − α f ′ ( z ) f ( z ) 1 − α | < β π 2 . We give sharp estimates for various coefficient problems for functions in B 1(α, β), which unify and extend well-known results for starlike functions, strongly starlike functions and functions whose derivative has positive real part in domain D.

scholarly journals On a Subclass of Multivalent Functions with Bounded Positive Real Part

2019 ◽  
Vol 7 (1) ◽  
pp. 1
Author(s):  
Thirupathi Ganapathi
Keyword(s):  
Differential Subordination ◽  
Positive Real Part ◽  
Integral Representations ◽  
Positive Real ◽  
Symmetric Points ◽  
Bounded Positive Real Part

In the present paper, by introducing a new subclass of multivalent functions with respect to - symmetric points, we have obtained the integral representations and conditions for starlikeness using differential subordination.

scholarly journals On the Fekete–Szegö Type Functionals for Close-to-Convex Functions

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1497 ◽  
Author(s):  
Katarzyna Tra̧bka-Wiȩcław ◽  
Paweł Zaprawa ◽  
Magdalena Gregorczyk ◽  
Andrzej Rysak
Keyword(s):  
Analytic Function ◽  
Real Number ◽  
Convex Functions ◽  
Univalent Functions ◽  
Starlike Functions ◽  
Positive Real Part ◽  
Positive Real ◽  
Hankel Determinants ◽  
Coefficient Problems ◽  
Theoretical Results

In this paper, we consider two functionals of the Fekete–Szegö type Θ f ( μ ) = a 4 − μ a 2 a 3 and Φ f ( μ ) = a 2 a 4 − μ a 3 2 for a real number μ and for an analytic function f ( z ) = z + a 2 z 2 + a 3 z 3 + … , | z | < 1 . This type of research was initiated by Hayami and Owa in 2010. They obtained results for functions satisfying one of the conditions Re f ( z ) / z > α or Re f ′ ( z ) > α , α ∈ [ 0 , 1 ) . Similar estimates were also derived for univalent starlike functions and for univalent convex functions. We discuss Θ f ( μ ) and Φ f ( μ ) for close-to-convex functions such that f ′ ( z ) = h ( z ) / ( 1 − z ) 2 , where h is an analytic function with a positive real part. Many coefficient problems, among others estimating of Θ f ( μ ) , Φ f ( μ ) or the Hankel determinants for close-to-convex functions or univalent functions, are not solved yet. Our results broaden the scope of theoretical results connected with these functionals defined for different subclasses of analytic univalent functions.

scholarly journals Radius of starlikeness of certain analytic functions

2021 ◽  
Vol 71 (1) ◽  
pp. 83-104
Author(s):  
Asha Sebastian ◽  
V. Ravichandran
Keyword(s):  
Analytic Function ◽  
Analytic Functions ◽  
Starlike Functions ◽  
Positive Real Part ◽  
Open Unit ◽  
Open Unit Disk ◽  
Sine Function ◽  
Positive Real ◽  
Radius Of Starlikeness ◽  
Lemniscate Of Bernoulli

Abstract This paper studies analytic functions f defined on the open unit disk of the complex plane for which f/g and (1 + z)g/z are both functions with positive real part for some analytic function g. We determine radius constants of these functions to belong to classes of strong starlike functions, starlike functions of order α, parabolic starlike functions, as well as to the classes of starlike functions associated with lemniscate of Bernoulli, cardioid, lune, reverse lemniscate, sine function, exponential function and a particular rational function. The results obtained are sharp.

scholarly journals Starlikeness of certain non-univalent functions

2021 ◽  
Vol 11 (4) ◽  
Author(s):  
Adam Lecko ◽  
V. Ravichandran ◽  
Asha Sebastian
Keyword(s):  
Analytic Functions ◽  
Univalent Functions ◽  
Starlike Functions ◽  
Positive Real Part ◽  
The Other ◽  
Open Unit ◽  
Sigmoid Function ◽  
Open Unit Disk ◽  
Positive Real ◽  
Lemniscate Of Bernoulli

AbstractWe consider three classes of functions defined using the class $${\mathcal {P}}$$ P of all analytic functions $$p(z)=1+cz+\cdots $$ p ( z ) = 1 + c z + ⋯ on the open unit disk having positive real part and study several radius problems for these classes. The first class consists of all normalized analytic functions f with $$f/g\in {\mathcal {P}}$$ f / g ∈ P and $$g/(zp)\in {\mathcal {P}}$$ g / ( z p ) ∈ P for some normalized analytic function g and $$p\in {\mathcal {P}}$$ p ∈ P . The second class is defined by replacing the condition $$f/g\in {\mathcal {P}}$$ f / g ∈ P by $$|(f/g)-1|<1$$ | ( f / g ) - 1 | < 1 while the other class consists of normalized analytic functions f with $$f/(zp)\in {\mathcal {P}}$$ f / ( z p ) ∈ P for some $$p\in {\mathcal {P}}$$ p ∈ P . We have determined radii so that the functions in these classes to belong to various subclasses of starlike functions. These subclasses includes the classes of starlike functions of order $$\alpha $$ α , parabolic starlike functions, as well as the classes of starlike functions associated with lemniscate of Bernoulli, reverse lemniscate, sine function, a rational function, cardioid, lune, nephroid and modified sigmoid function.

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