An unified approach to the Fekete–Szegö problem

Kanas, S.

doi:10.1016/j.amc.2012.01.070

Cited by 55 publications

(28 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Also, Goyal and Goswami [8] obtained the initial coefficient bounds for a class defined by fractional derivatives. Some more important results on coefficient inequalities can be found in [9], [10] and [11].…”

Section: Introductionmentioning

confidence: 99%

Coefficient Estimates and Quasi-Subordination Properties Associated with Certain Subclasses of Analytic and Bi-Univalent Functions

Goyal¹,

Kumar

2015

Mathematica Slovaca

View full text Add to dashboard Cite

In the present paper, we obtain the estimates on initial coefficients of normalized analytic function f in the open unit disk with f and its inverse g = f −1 satisfying the conditions that zf (z)/f (z) and zg (z)/g(z) are both quasi-subordinate to a univalent function whose range is symmetric with respect to the real axis. Several related classes of functions are also considered, and connections to earlier known results are established.

show abstract

Section: Introductionmentioning

confidence: 99%

Coefficient Estimates and Quasi-Subordination Properties Associated with Certain Subclasses of Analytic and Bi-Univalent Functions

Goyal¹,

Kumar

2015

Mathematica Slovaca

View full text Add to dashboard Cite

show abstract

“…We choose to recall here the investigations (see [1,13,16,17,21]). The coefficient estimate problem for the class S , known as the Bieberbach conjecture [2], was settled by de Branges [4], who proved that for a function f (z) = z + +∞ k=2 a k z k in the class S , |a k | k for k = 2, 3, .…”

Section: Introductionmentioning

confidence: 99%

“…By setting u = (1, 0, ..., 0) T in (6) and (7) of Example 1, we deduce that the mappings f defined in (12) and (13) are in the class Q B (U n ).…”

mentioning

confidence: 97%

Fekete and Szegö problem for a subclass of quasi-convex mappings in several complex variables

Yang

Liu

et al. 2015

Front. Math. China

View full text Add to dashboard Cite

Let K be the familiar class of normalized convex functions in the unit disk. Keogh and Merkes proved the well-known result that max f ∈K |a 3 − λa 2 2 | max{1/3, |λ − 1|}, λ ∈ C, and the estimate is sharp for each λ. We investigate the corresponding problem for a subclass of quasi-convex mappings of type B defined on the unit ball in a complex Banach space or on the unit polydisk in C n . The proofs of these results use some restrictive assumptions, which in the case of one complex variable are automatically satisfied.Keywords Fekete-Szegö problem, quasi-convex mappings of type A, quasiconvex mappings of type B, quasi-convex mappings of type C MSC 32A30, 32H02, 30C45

show abstract

“…In 1976, the -th Hankel determinant was stated for integers 1 and 1 [16], as follows: where the Hankel determinant 1 is called the Fekete-Szegö functional and 2 is defined as the second Hankel determinant functional. Recently, several researchers have investigated similar problems in this direction, [18][19][20][21][22][23][24][25][26][27] to name a few. Definition 1.1.…”

Section: Introductionmentioning

confidence: 99%

The Second Hankel Determinant Problem for a Class of Bi-Univalent Functions

2019

View full text Add to dashboard Cite

Hankel matrices are related to a wide range of disparate determinant computations and algorithms and some very attractive computational properties are allocated to them. Also, the Hankel determinants are crucial factors in the research of singularities and power series with integral coefficients. It is specified that the Fekete-Szegö functional and the second Hankel determinant are equivalent to 2 and 2 , respectively. In this study, the upper bounds were obtained for the second Hankel determinant of the subclass of bi-univalent functions, which is defined by subordination. It is worth noticing that the bounds rendered in the present paper generalize and modify some previous results.

show abstract

An unified approach to the Fekete–Szegö problem

Cited by 55 publications

References 6 publications

Coefficient Estimates and Quasi-Subordination Properties Associated with Certain Subclasses of Analytic and Bi-Univalent Functions

Coefficient Estimates and Quasi-Subordination Properties Associated with Certain Subclasses of Analytic and Bi-Univalent Functions

Fekete and Szegö problem for a subclass of quasi-convex mappings in several complex variables

The Second Hankel Determinant Problem for a Class of Bi-Univalent Functions

Contact Info

Product

Resources

About