scholarly journals Bohr Radius Problems for Some Classes of Analytic Functions Using Quantum Calculus Approach

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 623 ◽  
Author(s):  
Om Ahuja ◽  
Swati Anand ◽  
Naveen Kumar Jain
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Bohr Radius ◽  
Quantum Calculus ◽  
Radius Problems

The main purpose of this investigation is to use quantum calculus approach and obtain the Bohr radius for the class of q-starlike (q-convex) functions of order α . The Bohr radius is also determined for a generalized class of q-Janowski starlike and q-Janowski convex functions with negative coefficients.

scholarly journals On Quantum Differential Subordination Related with Certain Family of Analytic Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Afis Saliu ◽  
Khalida Inayat Noor ◽  
Saqib Hussain ◽  
Maslina Darus
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Quantum Calculus ◽  
Coefficient Inequality

Recently, there is a rapid increase of research in the area of Quantum calculus (known as q -calculus) due to its widespread applications in many areas of study, such as geometric functions theory. To this end, using the concept of q -conic domains of Janowski type as well as q - calculus, new subclasses of analytic functions are introduced. This family of functions extends the notion of α -convex and quasi-convex functions. Furthermore, a coefficient inequality, sufficiency criteria, and covering results for these novel classes are derived. Besides, some remarkable consequences of our investigation are highlighted.

scholarly journals Sharp Bohr Radius Constants for Certain Analytic Functions

2021 ◽  
Vol 44 (3) ◽  
pp. 1771-1785
Author(s):  
Swati Anand ◽  
Naveen Kumar Jain ◽  
Sushil Kumar
Keyword(s):  
Analytic Functions ◽  
Bohr Radius

scholarly journals Quasi-Hadamard Product of Certainω-Starlike andω-Convex Functions with respect to Symmetric Points

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Huo Tang ◽  
Guan-Tie Deng
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Hadamard Product ◽  
Symmetric Points

The main purpose of this paper is to derive some results associated with the quasi-Hadamard product of certainω-starlike andω-convex univalent analytic functions with respect to symmetric points.

Majorization of starlike and convex functions of complex order involving linear operators

2016 ◽  
Vol 66 (1) ◽  
Author(s):  
G. Murugusundaramoorthy ◽  
K. Thilagavathi
Keyword(s):  
Linear Operator ◽  
Convex Functions ◽  
Analytic Functions ◽  
Linear Operators ◽  
Starlike And Convex Functions ◽  
Complex Order

AbstractThe main object of this present paper is to investigate the problem of majorization of certain class of analytic functions of complex order defined by the Dziok-Raina linear operator. Moreover we point out some new or known consequences of our main result.

scholarly journals Fekete–Szegö problem for certain subclasses of analytic functions

2012 ◽  
Vol 45 (4) ◽  
Author(s):  
Halit Orhan ◽  
Erhan Deniz ◽  
Murat Çağlar
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Starlike And Convex Functions ◽  
Complex Order

AbstractIn this present investigation, authors introduce certain subclasses of starlike and convex functions of complex order

THE SHARP BOUND FOR THE HANKEL DETERMINANT OF THE THIRD KIND FOR CONVEX FUNCTIONS

2018 ◽  
Vol 97 (3) ◽  
pp. 435-445 ◽  
Author(s):  
BOGUMIŁA KOWALCZYK ◽  
ADAM LECKO ◽  
YOUNG JAE SIM
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Sharp Inequality ◽  
Sharp Bound ◽  
Hankel Determinant ◽  
The Third ◽  
Image Position

We prove the sharp inequality $|H_{3,1}(f)|\leq 4/135$ for convex functions, that is, for analytic functions $f$ with $a_{n}:=f^{(n)}(0)/n!,~n\in \mathbb{N}$, such that $$\begin{eqnarray}Re\bigg\{1+\frac{zf^{\prime \prime }(z)}{f^{\prime }(z)}\bigg\}>0\quad \text{for}~z\in \mathbb{D}:=\{z\in \mathbb{C}:|z|<1\},\end{eqnarray}$$ where $H_{3,1}(f)$ is the third Hankel determinant $$\begin{eqnarray}H_{3,1}(f):=\left|\begin{array}{@{}ccc@{}}a_{1} & a_{2} & a_{3}\\ a_{2} & a_{3} & a_{4}\\ a_{3} & a_{4} & a_{5}\end{array}\right|.\end{eqnarray}$$

scholarly journals On Certain Classes of Convex Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Young Jae Sim ◽  
Oh Sang Kwon
Keyword(s):  
Unit Disk ◽  
Convex Functions ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Real Numbers ◽  
Inverse Functions

For real numbersαandβsuch that0≤α<1<β, we denote by𝒦α,βthe class of normalized analytic functions which satisfy the following two sided-inequality:α<ℜ1+zf′′z/f′z<β  z∈𝕌,where𝕌denotes the open unit disk. We find some relationships involving functions in the class𝒦(α,β). And we estimate the bounds of coefficients and solve the Fekete-Szegö problem for functions in this class. Furthermore, we investigate the bounds of initial coefficients of inverse functions or biunivalent functions.

Bohr Radius for Classes of Analytic Functions

2019 ◽  
Vol 74 (4) ◽  
Author(s):  
Rosihan M. Ali ◽  
Naveen Kumar Jain ◽  
Vaithiyanathan Ravichandran
Keyword(s):  
Analytic Functions ◽  
Bohr Radius

scholarly journals Uniformly Alpha-Quasi-Convex Functions Defined by Janowski Functions

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Shahid Mahmood ◽  
Sarfraz Nawaz Malik ◽  
Sumbal Farman ◽  
S. M. Jawwad Riaz ◽  
Shabieh Farwa
Keyword(s):  
Integral Representation ◽  
Convex Functions ◽  
Analytic Functions ◽  
Janowski Functions ◽  
Convolution Properties ◽  
Inclusion Results

In this work, we aim to introduce and study a new subclass of analytic functions related to the oval and petal type domain. This includes various interesting properties such as integral representation, sufficiency criteria, inclusion results, and the convolution properties for newly introduced class.

scholarly journals Note on Neighborhoods of Some Classes of Analytic Functions with Negative Coefficients

2011 ◽  
Vol 2011 ◽  
pp. 1-7
Author(s):  
Irina Dorca ◽  
Mugur Acu ◽  
Daniel Breaz
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Starlike And Convex Functions ◽  
Inclusion Relations

In this paper, we prove several inclusion relations associated with the (n,δ) neighborhoods of some subclasses of starlike and convex functions with negative coefficients.

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