scholarly journals On Coefficient Problems for Functions Connected with the Sine Function

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1179
Author(s):  
Katarzyna Tra̧bka-Wiȩcław
Keyword(s):  
Analytic Functions ◽  
Sine Function ◽  
Hankel Determinant ◽  
Coefficient Problems ◽  
Logarithmic Coefficients ◽  
Symmetric Points

In this paper, some coefficient problems for starlike analytic functions with respect to symmetric points are considered. Bounds of several coefficient functionals for functions belonging to this class are provided. The main aim of this paper is to find estimates for the following: coefficients, logarithmic coefficients, some cases of the generalized Zalcman coefficient functional, and some cases of the Hankel determinant.

scholarly journals Third Hankel determinant and Zalcman functional for a class of starlike functions with respect to symmetric points related with sine function

2021 ◽  
Vol 25 (01) ◽  
pp. 29-36
Author(s):  
Muhammad Ghaffar Khan ◽  
Bakhtiar Ahmad ◽  
Gangadharan Murugusundaramoorthy ◽  
Wali Khan Mashwani ◽  
Sibel Yalçin ◽  
...  
Keyword(s):  
Starlike Functions ◽  
Sine Function ◽  
Hankel Determinant ◽  
Symmetric Points

scholarly journals Coefficient Problems in a Class of Functions with Bounded Turning Associated with Sine Function

2021 ◽  
Vol 14 (1) ◽  
pp. 53-64
Author(s):  
Muhammad Ghaffar Khan ◽  
Bakhtiar Ahmad ◽  
Janusz Sokol ◽  
Zubair Muhammad ◽  
Wali Khan Mashwani ◽  
...  
Keyword(s):  
Power Series ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Sine Function ◽  
Hankel Determinant ◽  
Hankel Determinants ◽  
The Third ◽  
Coefficient Problems ◽  
Bounded Turning ◽  
Class Of Functions

The Hankel determinant for a function having power series was first defined by Pommerenke. The growth of Hankel determinant has been evaluated for different subcollections of univalent functions. Many subclasses with bounded turning are several interesting geometric properties. In this paper, some classes of functions with bounded turning which connect to the sine function are studied in the region of the unit disc in order. Our purpose is to obtain some upper bounds for the third and fourth Hankel determinants related to such classes.

scholarly journals Some Properties of a Generalized Class of Analytic Functions Related with Janowski Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
M. Arif ◽  
K. I. Noor ◽  
M. Raza ◽  
W. Haq
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Arc Length ◽  
Hankel Determinant ◽  
Janowski Functions ◽  
Coefficient Problems ◽  
Number Of Classes

We define a classT̃k[A, B,α,ρ] of analytic functions by using Janowski’s functions which generalizes a number of classes studied earlier such as the class of strongly close-to-convex functions. Some properties of this class, including arc length, coefficient problems, and a distortion result, are investigated. We also discuss the growth of Hankel determinant problem.

scholarly journals Hankel determinant of order three for familiar subsets of analytic functions related with sine function

2019 ◽  
Vol 17 (1) ◽  
pp. 1615-1630 ◽  
Author(s):  
Muhammad Arif ◽  
Mohsan Raza ◽  
Huo Tang ◽  
Shehzad Hussain ◽  
Hassan Khan
Keyword(s):  
Unit Disk ◽  
Complex Plane ◽  
Analytic Functions ◽  
Sine Function ◽  
Hankel Determinant ◽  
Sine Functions

Abstract In this paper we define and consider some familiar subsets of analytic functions associated with sine functions in the region of unit disk on the complex plane. For these classes our aim is to find the Hankel determinant of order three.

scholarly journals Initial logarithmic coefficients for functions starlike with respect to symmetric points

2021 ◽  
Vol 27 (3) ◽  
Author(s):  
Paweł Zaprawa
Keyword(s):  
Exact Result ◽  
Positive Real Part ◽  
Additional Benefit ◽  
Extremal Functions ◽  
Positive Real ◽  
Logarithmic Coefficients ◽  
Symmetric Points

AbstractIn this paper, we obtain the bounds of the initial logarithmic coefficients for functions in the classes $${\mathcal {S}}_S^*$$ S S ∗ and $${\mathcal {K}}_S$$ K S of functions which are starlike with respect to symmetric points and convex with respect to symmetric points, respectively. In our research, we use a different approach than the usual one in which the coeffcients of f are expressed by the corresponding coeffcients of functions with positive real part. In what follows, we express the coeffcients of f in $${\mathcal {S}}_S^*$$ S S ∗ and $${\mathcal {K}}_S$$ K S by the corresponding coeffcients of Schwarz functions. In the proofs, we apply some inequalities for these functions obtained by Prokhorov and Szynal, by Carlson and by Efraimidis. This approach offers a additional benefit. In many cases, it is easily possible to predict the exact result and to select extremal functions. It is the case for $${\mathcal {S}}_S^*$$ S S ∗ and $${\mathcal {K}}_S$$ K S .

Third Hankel determinants for two classes of analytic functions with real coefficients

2021 ◽  
Vol 33 (4) ◽  
pp. 973-986
Author(s):  
Young Jae Sim ◽  
Paweł Zaprawa
Keyword(s):  
Analytic Functions ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Hankel Determinant ◽  
Lower And Upper Bounds ◽  
Hankel Determinants ◽  
The Third ◽  
Typically Real ◽  
Class Of Functions ◽  
Typically Real Functions

Abstract In recent years, the problem of estimating Hankel determinants has attracted the attention of many mathematicians. Their research have been focused mainly on deriving the bounds of H 2 , 2 {H_{2,2}} or H 3 , 1 {H_{3,1}} over different subclasses of 𝒮 {\mathcal{S}} . Only in a few papers third Hankel determinants for non-univalent functions were considered. In this paper, we consider two classes of analytic functions with real coefficients. The first one is the class 𝒯 {\mathcal{T}} of typically real functions. The second object of our interest is 𝒦 ℝ ⁢ ( i ) {\mathcal{K}_{\mathbb{R}}(i)} , the class of functions with real coefficients which are convex in the direction of the imaginary axis. In both classes, we find lower and upper bounds of the third Hankel determinant. The results are sharp.

scholarly journals The Sharp Bound of the Hankel Determinant of the Third Kind for Starlike Functions with Real Coefficients

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 721 ◽  
Author(s):  
Oh Sang Kwon ◽  
Young Jae Sim
Keyword(s):  
Analytic Functions ◽  
Starlike Functions ◽  
Sharp Bound ◽  
Hankel Determinant ◽  
The Third

Let SR * be the class of starlike functions with real coefficients, i.e., the class of analytic functions f which satisfy the condition f ( 0 ) = 0 = f ′ ( 0 ) − 1 , Re { z f ′ ( z ) / f ( z ) } > 0 , for z ∈ D : = { z ∈ C : | z | < 1 } and a n : = f ( n ) ( 0 ) / n ! is real for all n ∈ N . In the present paper, it is obtained that the sharp inequalities − 4 / 9 ≤ H 3 , 1 ( f ) ≤ 3 / 9 hold for f ∈ SR * , where H 3 , 1 ( f ) is the third Hankel determinant of order 3 defined by H 3 , 1 ( f ) = a 3 ( a 2 a 4 − a 3 2 ) − a 4 ( a 4 − a 2 a 3 ) + a 5 ( a 3 − a 2 2 ) .

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.

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