scholarly journals Coefficient Inequalities of Functions Associated with Petal Type Domains

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 298 ◽  
Author(s):  
Sarfraz Malik ◽  
Shahid Mahmood ◽  
Mohsan Raza ◽  
Sumbal Farman ◽  
Saira Zainab
Keyword(s):  
Taylor Series ◽  
Upper Bound ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Series Representation ◽  
Functional Inequalities ◽  
Major Interest ◽  
Coefficient Inequalities ◽  
Inverse Functions ◽  
Analytic And Univalent Functions

In the theory of analytic and univalent functions, coefficients of functions’ Taylor series representation and their related functional inequalities are of major interest and how they estimate functions’ growth in their specified domains. One of the important and useful functional inequalities is the Fekete-Szegö inequality. In this work, we aim to analyze the Fekete-Szegö functional and to find its upper bound for certain analytic functions which give parabolic and petal type regions as image domains. Coefficient inequalities and the Fekete-Szegö inequality of inverse functions to these certain analytic functions are also established in this work.

scholarly journals Coefficient Inequalities of Functions Associated with Hyperbolic Domains

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 88 ◽  
Author(s):  
Sarfraz Malik ◽  
Shahid Mahmood ◽  
Mohsan Raza ◽  
Sumbal Farman ◽  
Saira Zainab ◽  
...  
Keyword(s):  
Upper Bound ◽  
Analytic Functions ◽  
Upper Bounds ◽  
Image Domain ◽  
Coefficient Inequalities ◽  
Inverse Functions ◽  
Hyperbolic Domains

In this work, our focus is to study the Fekete-Szegö functional in a different and innovative manner, and to do this we find its upper bound for certain analytic functions which give hyperbolic regions as image domain. The upper bounds obtained in this paper give refinement of already known results. Moreover, we extend our work by calculating similar problems for the inverse functions of these certain analytic functions for the sake of completeness.

scholarly journals Coefficient inequalities for a class of analytic functions associated with the lemniscate of Bernoulli

2018 ◽  
Vol 37 (4) ◽  
pp. 83-95
Author(s):  
Trailokya Panigrahi ◽  
Janusz Sokól
Keyword(s):  
Upper Bound ◽  
Analytic Functions ◽  
Hankel Determinant ◽  
Lemniscate Of Bernoulli ◽  
Toeplitz Determinant ◽  
Second Hankel Determinant ◽  
Coefficient Inequalities ◽  
The Right

In this paper, a new subclass of analytic functions ML_{\lambda}^{*}  associated with the right half of the lemniscate of Bernoulli is introduced. The sharp upper bound for the Fekete-Szego functional |a_{3}-\mu a_{2}^{2}|  for both real and complex \mu are considered. Further, the sharp upper bound to the second Hankel determinant |H_{2}(1)| for the function f in the class ML_{\lambda}^{*} using Toeplitz determinant is studied. Relevances of the main results are also briefly indicated.

Application of fractional calculus operators for a new class of univalent functions with negative coefficients defined by Hohlov operator

2010 ◽  
Vol 60 (1) ◽  
Author(s):  
Waggas Atshan
Keyword(s):  
Fractional Calculus ◽  
Unit Disc ◽  
Univalent Functions ◽  
Distortion Theorem ◽  
New Class ◽  
Fractional Calculus Operators ◽  
Coefficient Inequalities ◽  
Analytic And Univalent Functions

AbstractIn this paper, we introduce a new class W(a, b, c, γ, β) which consists of analytic and univalent functions with negative coefficients in the unit disc defined by Hohlov operator, we obtain distortion theorem using fractional calculus techniques for this class. Also coefficient inequalities and some results for this class are obtained.

scholarly journals Convolution properties for subclasses of meromorphic univalent functions of complex order

Filomat ◽  
2012 ◽  
Vol 26 (1) ◽  
pp. 153-163 ◽  
Author(s):  
Teodor Bulboacă ◽  
Mohamed Aouf ◽  
Rabha El-Ashwah
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Complex Order ◽  
Inclusion Relations ◽  
Coefficient Inequalities ◽  
Convolution Properties ◽  
Meromorphic Univalent Functions

Using the new linear operator Lm(?,l)f(z) = 1/z + ??k=1(l/l+ ?k)m akzk-1, f ? ?, where l > 0, ? ? 0, and m ? N0 = N ? {0}, we introduce two subclasses of meromorphic analytic functions, and we investigate several convolution properties, coefficient inequalities, and inclusion relations for these classes.

AN APPLICATION OF SCHUR’S ALGORITHM TO VARIABILITY REGIONS OF CERTAIN ANALYTIC FUNCTIONS II

2021 ◽  
pp. 1-14
Author(s):  
MD FIROZ ALI ◽  
VASUDEVARAO ALLU ◽  
HIROSHI YANAGIHARA
Keyword(s):  
Analytic Functions ◽  
Univalent Functions ◽  
Convex Domains ◽  
Schur Algorithm ◽  
Variability Region ◽  
Analytic And Univalent Functions

Abstract We extend our study of variability regions, Ali et al. [‘An application of Schur algorithm to variability regions of certain analytic functions–I’, Comput. Methods Funct. Theory, to appear] from convex domains to starlike domains. Let $\mathcal {CV}(\Omega )$ be the class of analytic functions f in ${\mathbb D}$ with $f(0)=f'(0)-1=0$ satisfying $1+zf''(z)/f'(z) \in {\Omega }$ . As an application of the main result, we determine the variability region of $\log f'(z_0)$ when f ranges over $\mathcal {CV}(\Omega )$ . By choosing a particular $\Omega $ , we obtain the precise variability regions of $\log f'(z_0)$ for some well-known subclasses of analytic and univalent functions.

scholarly journals LOGARITHMIC COEFFICIENTS PROBLEMS IN FAMILIES RELATED TO STARLIKE AND CONVEX FUNCTIONS

2019 ◽  
Vol 109 (2) ◽  
pp. 230-249 ◽  
Author(s):  
SAMINATHAN PONNUSAMY ◽  
NAVNEET LAL SHARMA ◽  
KARL-JOACHIM WIRTHS
Keyword(s):  
Upper Bound ◽  
Convex Functions ◽  
Univalent Functions ◽  
List Type ◽  
Starlike And Convex Functions ◽  
The Family ◽  
Logarithmic Coefficients ◽  
Dilogarithm Function ◽  
Image Position ◽  
Analytic And Univalent Functions

Let${\mathcal{S}}$be the family of analytic and univalent functions$f$in the unit disk$\mathbb{D}$with the normalization$f(0)=f^{\prime }(0)-1=0$, and let$\unicode[STIX]{x1D6FE}_{n}(f)=\unicode[STIX]{x1D6FE}_{n}$denote the logarithmic coefficients of$f\in {\mathcal{S}}$. In this paper we study bounds for the logarithmic coefficients for certain subfamilies of univalent functions. Also, we consider the families${\mathcal{F}}(c)$and${\mathcal{G}}(c)$of functions$f\in {\mathcal{S}}$defined by$$\begin{eqnarray}\text{Re}\biggl(1+{\displaystyle \frac{zf^{\prime \prime }(z)}{f^{\prime }(z)}}\biggr)>1-{\displaystyle \frac{c}{2}}\quad \text{and}\quad \text{Re}\biggl(1+{\displaystyle \frac{zf^{\prime \prime }(z)}{f^{\prime }(z)}}\biggr)<1+{\displaystyle \frac{c}{2}},\quad z\in \mathbb{D},\end{eqnarray}$$for some$c\in (0,3]$and$c\in (0,1]$, respectively. We obtain the sharp upper bound for$|\unicode[STIX]{x1D6FE}_{n}|$when$n=1,2,3$and$f$belongs to the classes${\mathcal{F}}(c)$and${\mathcal{G}}(c)$, respectively. The paper concludes with the following two conjectures:∙If$f\in {\mathcal{F}}(-1/2)$, then$|\unicode[STIX]{x1D6FE}_{n}|\leq 1/n(1-(1/2^{n+1}))$for$n\geq 1$, and$$\begin{eqnarray}\mathop{\sum }_{n=1}^{\infty }|\unicode[STIX]{x1D6FE}_{n}|^{2}\leq {\displaystyle \frac{\unicode[STIX]{x1D70B}^{2}}{6}}+{\displaystyle \frac{1}{4}}~\text{Li}_{2}\biggl({\displaystyle \frac{1}{4}}\biggr)-\text{Li}_{2}\biggl({\displaystyle \frac{1}{2}}\biggr),\end{eqnarray}$$where$\text{Li}_{2}(x)$denotes the dilogarithm function.∙If$f\in {\mathcal{G}}(c)$, then$|\unicode[STIX]{x1D6FE}_{n}|\leq c/2n(n+1)$for$n\geq 1$.

Coefficient Estimates for a Subclass of Bi-Univalent Functions Defined by q-Derivative Operator

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 306 ◽  
Author(s):  
Suhila Elhaddad ◽  
Maslina Darus
Keyword(s):  
Unit Disk ◽  
Systematic Study ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Derivative Operator ◽  
Coefficient Bounds ◽  
Coefficient Inequalities

Recently, a number of features and properties of interest for a range of bi-univalent and univalent analytic functions have been explored through systematic study, e.g., coefficient inequalities and coefficient bounds. This study examines S q δ ( ϑ , η , ρ , ν ; ψ ) as a novel general subclass of Σ which comprises normalized analytic functions, as well as bi-univalent functions within Δ as an open unit disk. The study locates estimates for the | a 2 | and | a 3 | Taylor–Maclaurin coefficients in functions of the class which is considered. Additionally, links with a number of previously established findings are presented.

scholarly journals On Subclass of Analytic Univalent Functions Associated with Negative Coefficients

2010 ◽  
Vol 2010 ◽  
pp. 1-11
Author(s):  
Ma'moun Harayzeh Al-Abbadi ◽  
Maslina Darus
Keyword(s):  
Analytic Functions ◽  
Univalent Functions ◽  
Extreme Points ◽  
Open Unit ◽  
Derivative Operator ◽  
Generalized Derivative ◽  
Closure Theorems ◽  
Coefficient Inequalities ◽  
Distortion Theorems ◽  
Growth And Distortion Theorems

M. H. Al-Abbadi and M. Darus (2009) recently introduced a new generalized derivative operatorμλ1,λ2n,m, which generalized many well-known operators studied earlier by many different authors. In this present paper, we shall investigate a new subclass of analytic functions in the open unit diskU={z∈ℂ:|z|<1}which is defined by new generalized derivative operator. Some results on coefficient inequalities, growth and distortion theorems, closure theorems, and extreme points of analytic functions belonging to the subclass are obtained.

scholarly journals Upper Bound of Second Hankel Determinant for Certain Subclasses of Analytic Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ming-Sheng Liu ◽  
Jun-Feng Xu ◽  
Ming Yang
Keyword(s):  
Upper Bound ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Hankel Determinant ◽  
Second Hankel Determinant ◽  
Work Done

In this present investigation, we first give a survey of the work done so far in this area of Hankel determinant for univalent functions. Then the upper bounds of the second Hankel determinant|a2a4−a32|for functions belonging to the subclassesS(α,β),K(α,β),Ss∗(α,β), andKs(α,β)of analytic functions are studied. Some of the results, presented in this paper, would extend the corresponding results of earlier authors.

scholarly journals A novel subclass of analytic functions specified by a family of fractional derivatives in the complex domain

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2837-2849
Author(s):  
Zainab Esa ◽  
H.M. Srivastava ◽  
Adem Kılıçman ◽  
Rabha Ibrahim
Keyword(s):  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Univalent Functions ◽  
Complex Domain ◽  
Open Unit ◽  
Coefficient Estimates ◽  
Fractional Derivative Operators ◽  
Coefficient Inequalities ◽  
Distortion Theorems ◽  
Analytic And Univalent Functions

In this paper, by making use of a certain family of fractional derivative operators in the complex domain, we introduce and investigate a new subclass P?,?(k,?,?) of analytic and univalent functions in the open unit disk U. In particular, for functions in the class P?,?(k,?,?), we derive sufficient coefficient inequalities and coefficient estimates, distortion theorems involving the above-mentioned fractional derivative operators, and the radii of starlikeness and convexity. In addition, some applications of functions in the class P?,?(k,?,?) are also pointed out.

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