Initial successive coefficients for certain classes of univalent functions involving the exponential function

Shi, Lei; Wang, Zhi-Gang; Su, Ren-Li; Arif, Muhammad

doi:10.7153/jmi-2020-14-77

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Definition 1 [19]a Function P (Z) Is Said To Be In the Class1

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“….It is well-known that the Fekete-Szegö functional a 1 -a 2 0 is H 2,1 f . Fekete-Szegö then further generalized the estimate a 1µa 2 0 with µ real and f (z) ∈ S. Moreover, we also know that the functional a 0 a 2 -a 2 1 is equivalent to H 2,1 f .In particular, sharp upper bounds on H 2, (2) were obtained by the authors of articles [23,24] for various classes of functions. In the present investigation, we study the upper bound of H 4,1 f for a subclass K -SL a, b of analytic functions by using Hankel determinants.…”

Section: Definition 1 [19]a Function P (Z) Is Said To Be In the Classmentioning

confidence: 88%

A Study of Fourth Hankel Determinant of Certain Analytic Function

Khan,

Frasin

et al. 2021

VFAST trans. math.

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Section: Definition 1 [19]a Function P (Z) Is Said To Be In the Classmentioning

confidence: 88%

A Study of Fourth Hankel Determinant of Certain Analytic Function

Khan,

Frasin

et al. 2021

VFAST trans. math.

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Sharp Bounds on Hankel Determinants for Certain Subclass of Starlike Functions

Wang¹,

Arif²,

Liu³

et al. 2023

jaac

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Coefficient Estimates for a Subclass of Starlike Functions

Răducanu

2020

Mathematics

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In this note, we consider a subclass H3/2(p) of starlike functions f with f″(0)=p for a prescribed p∈[0,2]. Usually, in the study of univalent functions, estimates on the Taylor coefficients, Fekete–Szegö functional or Hankel determinats are given. Another coefficient problem which has attracted considerable attention is to estimate the moduli of successive coefficients |an+1|−|an|. Recently, the related functional |an+1−an| for the initial successive coefficients has been investigated for several classes of univalent functions. We continue this study and for functions f(z)=z+∑n=2∞anzn∈H3/2(p), we investigate upper bounds of initial coefficients and the difference of moduli of successive coefficients |a3−a2| and |a4−a3|. Estimates of the functionals |a2a4−a32| and |a4−a2a3| are also derived. The obtained results expand the scope of the theoretical results related with the functional |an+1−an| for various subclasses of univalent functions.

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Initial successive coefficients for certain classes of univalent functions involving the exponential function

Cited by 5 publications

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A Study of Fourth Hankel Determinant of Certain Analytic Function

A Study of Fourth Hankel Determinant of Certain Analytic Function

Sharp Bounds on Hankel Determinants for Certain Subclass of Starlike Functions

Coefficient Estimates for a Subclass of Starlike Functions

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