Properties of q-Symmetric Starlike Functions of Janowski Type

Saliu, Afis; Al-Shbeil, Isra; Gong, Jianhua; Aloraini, Najla

doi:10.3390/sym14091907

Cited by 24 publications

(15 citation statements)

References 24 publications

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“…The complexity of the challenge significantly increases when addressing the scenario where r = 3 as opposed to r = 2. Babalola [7] was the pioneer in attempting to establish an upper bound for |H 3,1 (f)| across the domains of ℜ, S * , and K. In recent times, multiple researchers have actively pursued the task of determining a upper bound for |H 3,1 (f)| (see [2,3,4,5,6,8,20,21,22,23,24,25])…”

Section: Introductionmentioning

confidence: 99%

Some Coefficient of Inequility for Subclass Of holomorphic Functions

Al-shbeil,

RATH,

ALHEFTHI

et al. 2024

Preprint

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Since the early twentieth century, the investigation of bound fordeterminant of Hankel matrices in analytic univalent functions has been a focalpoint for mathematical research, providing a rich avenue for the exploration ofgeometric properties. Over the years, numerous researchers have striven to establishupper bounds for determinant of the third order Hankel matrix withinvarious subclasses of analytic univalent functions. While these efforts haveyielded valuable insights, the attainment of sharp bounds remained a challengeuntil Know et al. (2018) achieved an exact estimation of the fourth coefficientin the Carath´eodory class. In more recent developments, investigators haveleveraged this precise estimation of the fourth coefficient, alongside the welldefinedvalues of the second and third coefficients within the Carath´eodoryclass. This breakthrough has empowered them to delineate sharp bounds forthe third Hankel determinant in diverse subclasses of analytic univalent functions.This present study embarks on an exploration of upper bounds for thesecond-order Hankel determinant within the realm of analytic functions, subjectto the normalized conditions of f(0) = 0 and f′(0) = 1. We further extendour investigation to specific sub-classes of holomorphic functions, culminatingin the derivation of sharp bounds for a parameter of particular interest. 2020 Mathematics Subject Classification. 30C45, 30C50.

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Section: Introductionmentioning

confidence: 99%

Some Coefficient of Inequility for Subclass Of holomorphic Functions

Al-shbeil,

RATH,

ALHEFTHI

et al. 2024

Preprint

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“…The subject of q-calculus has drawn the interest of several researchers in recent years, and the papers [21][22][23] contain a variety of new observations. Further current details on convex and starlike functions with regard to their symmetric points can be found in [24,25] and the references therein. As a consequence of ongoing research on differential and integral operators, we in this study present a novel fractional differential operator.…”

Section: Introduction Definitions and Motivationmentioning

confidence: 99%

Faber Polynomial Coefficient Estimates for Bi-Close-to-Convex Functions Defined by the q-Fractional Derivative

Srivástava

Al-Shbeil

Xin

et al. 2023

Axioms

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By utilizing the concept of the q-fractional derivative operator and bi-close-to-convex functions, we define a new subclass of A, where the class A contains normalized analytic functions in the open unit disk E and is invariant or symmetric under rotation. First, using the Faber polynomial expansion (FPE) technique, we determine the lth coefficient bound for the functions contained within this class. We provide a further explanation for the first few coefficients of bi-close-to-convex functions defined by the q-fractional derivative. We also emphasize upon a few well-known outcomes of the major findings in this article.

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“…Remarkably, as q approaches 1, the D q reduces to the classical derivative. For more details and recent applications of the q-fractional derivative, we refer the readers to [15][16][17][18][19][20][21] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Coefficient Inequalities of q-Bi-Univalent Mappings Associated with q-Hyperbolic Tangent Function

Shaba,

Araci,

et al. 2023

Fractal Fract

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The present study introduces a new family of analytic functions by utilizing the q-derivative operator and the q-version of the hyperbolic tangent function. We find certain inequalities, including the coefficient bounds, second Hankel determinants, and Fekete–Szegö inequalities, for this novel family of bi-univalent functions. It is worthy of note that almost all the results are sharp, and their corresponding extremal functions are presented. In addition, some special cases are demonstrated to show the validity of our findings.

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Properties of q-Symmetric Starlike Functions of Janowski Type

Cited by 24 publications

References 24 publications

Some Coefficient of Inequility for Subclass Of holomorphic Functions

Some Coefficient of Inequility for Subclass Of holomorphic Functions

Faber Polynomial Coefficient Estimates for Bi-Close-to-Convex Functions Defined by the q-Fractional Derivative

Coefficient Inequalities of q-Bi-Univalent Mappings Associated with q-Hyperbolic Tangent Function

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