Hankel determinant for starlike and convex functions of order alpha

Krishna, D. Vamshee; RamReddy, T.

doi:10.32513/tbilisi/1528768890

Cited by 20 publications

(20 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where a 1 = 1. For brief history of Hankel determinant (see [30] [15] generalized the result from [11] giving the sharp bound of |H 2 (2)| in the class of starlike and convex functions of α. P. Zaprawa [36] showed that if f ∈ T, the class of typically real functions, then |H 2 (2)| ≤ 9. Apart from these, many research all over the globe obtained the upper bounds for various subclasses of univalent analytic functions and their results are available in literature (see [2,3,12,[22][23][24]).…”

Section: Introductionmentioning

confidence: 99%

Second Hankel determinant for a subclass of analytic functions defined by S$\check{a}$l$\check{a}$gean-difference operator

Panigrahi¹,

Murugusundaramoorthy²

2022

Mat. Stud.

View full text Add to dashboard Cite

In the present investigation, inspired by the work on Yamaguchi type class of analytic functions satisfyingthe analytic criteria $\mathfrak{Re}\{\frac{f (z)}{z}\} > 0, $ in the openunit disk $\Delta=\{z \in \mathbb{C}\colon |z|<1\}$ and making use of S\v{a}l\v{a}gean-difference operator, which is a special type of Dunkl operator with Dunkl constant $\vartheta$ in $\Delta$ , wedesignate definite new classes of analytic functions $\mathcal{R}_{\lambda}^{\beta}(\psi)$ in $\Delta$. For functionsin this new class , significantcoefficient estimates $|a_2|$ and $a_3|$ are obtained. Moreover, Fekete-Szeg\H{o} inequalities and second Hankel determinant for the function belonging to this class are derived. By fixing the parameters a number of special cases are developed are new (or generalization) of the results of earlier researchers in this direction.

show abstract

Section: Introductionmentioning

confidence: 99%

Second Hankel determinant for a subclass of analytic functions defined by S$\check{a}$l$\check{a}$gean-difference operator

Panigrahi¹,

Murugusundaramoorthy²

2022

Mat. Stud.

View full text Add to dashboard Cite

show abstract

“…On the other hand, the sharp bound of this determinant for the class of close-to-convex functions is unknown (see [9]). For more results on H 2,2 (f), see [10][11][12][13][14][15][16]. e estimation of |H 3,1 (f)| is much more difficult to obtain as compared to |H 2,2 (f)|.…”

Section: Introduction and Definitionsmentioning

confidence: 99%

Fourth Hankel Determinant for the Set of Star-Like Functions

Arif

rani

Raza

et al. 2021

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…In a view of this definition, a 2 a 4 − a 2 3 is the second Hankel determinant (more precisely, H 2 (2)). The sharp bounds of |a 2 a 4 − a 3 2 | for almost all important subclasses of the class S of analytic univalent functions were found (see, for example, [3][4][5][6][7][8]). It is worth noting that we still do not know the exact bound of this expression for S, nor for C consisting of all close-to-convex functions (see [9]).…”

Section: Introductionmentioning

confidence: 99%

On Coefficient Functionals for Functions with Coefficients Bounded by 1

2020

View full text Add to dashboard Cite

In this paper, we discuss two well-known coefficient functionals a 2 a 4 - a 3 2 and a 4 - a 2 a 3 . The first one is called the Hankel determinant of order 2. The second one is a special case of Zalcman functional. We consider them for functions in the class Q R ( 1 2 ) of analytic functions with real coefficients which satisfy the condition ( ) f ( z ) z > 1 2 for z in the unit disk Δ . It is known that all coefficients of f ∈ Q R ( 1 2 ) are bounded by 1. We find the upper bound of a 2 a 4 - a 3 2 and the bound of | a 4 - a 2 a 3 | . We also consider a few subclasses of Q R ( 1 2 ) and we estimate the above mentioned functionals. In our research two different methods are applied. The first method connects the coefficients of a function in a given class with coefficients of a corresponding Schwarz function or a function with positive real part. The second method is based on the theorem of formulated by Szapiel. According to this theorem, we can point out the extremal functions in this problem, that is, functions for which equalities in the estimates hold. The obtained estimates significantly extend the results previously established for the discussed classes. They allow to compare the behavior of the coefficient functionals considered in the case of real coefficients and arbitrary coefficients.

show abstract

Hankel determinant for starlike and convex functions of order alpha

Cited by 20 publications

References 8 publications

Second Hankel determinant for a subclass of analytic functions defined by S$\check{a}$l$\check{a}$gean-difference operator

Second Hankel determinant for a subclass of analytic functions defined by S$\check{a}$l$\check{a}$gean-difference operator

Fourth Hankel Determinant for the Set of Star-Like Functions

On Coefficient Functionals for Functions with Coefficients Bounded by 1

Contact Info

Product

Resources

About