Coefficient-Related Studies and Fekete-Szegö Type Inequalities for New Classes of Bi-Starlike and Bi-Convex Functions

One of the important problems regarding coefficients of analytical functions (i.e., Fekete–Szegö inequality) was raised by Fekete and Szegö in 1933. The results of this research are dedicated to determine upper coefficient estimates and the Fekete–Szegö problem in the class WΣ(δ,λ;ϑ), which is defined by generalized telephone numbers. We also indicate some specific conditions and consequences of results found by us.

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“…When δ = 0 and λ = 1 Theorem 2 leads to the known result on Cotîrlǎ and Wanas for the family C E (ϑ) (see [34]).…”

Section: Corollary 3 ([34]mentioning

confidence: 78%

“…When δ = λ = 0, the Theorem 1 is reduced to the corresponding results of Cotîrlǎ and Wanas (see [34]).…”

Section: Resultsmentioning

confidence: 95%

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On a Fekete–Szegö Problem Associated with Generalized Telephone Numbers

et al. 2023

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“…Finally, the class S * (e z ) was considered in [9]. For more studies, see the following articles [10][11][12][13][14][15][16][17][18][19][20][21].…”

Section: Introduction and Definitionsmentioning

confidence: 99%

New Applications of Fractional q-Calculus Operator for a New Subclass of q-Starlike Functions Related with the Cardioid Domain

Khan,

AbaOud

2024

Fractal Fract

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Recently, a number of researchers from different fields have taken a keen interest in the domain of fractional q-calculus on the basis of fractional integrals and derivative operators. This has been used in various scientific research and technology fields, including optics, mathematical biology, plasma physics, electromagnetic theory, and many more. This article explores some mathematical applications of the fractional q-differential and integral operator in the field of geometric function theory. By using the linear multiplier fractional q-differintegral operator Dq,λmρ,σ and subordination, we define and develop a collection of q-starlike functions that are linked to the cardioid domain. This study also investigates sharp inequality problems like initial coefficient bounds, the Fekete–Szego problems, and the coefficient inequalities for a new class of q-starlike functions in the open unit disc U. Furthermore, we analyze novel findings with respect to the inverse function (μ−1) within the class of q-starlike functions in U. The findings in this paper are easy to understand and show a connection between present and past studies.

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“…Furthermore, many authors (see, for example, Refs. [42][43][44][45][46][47][48][49][50][51]) applied the technique of Faber polynomials and determined some interesting results for bi-univalent functions (see, for details, Ref. [44]).…”

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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Coefficient-Related Studies and Fekete-Szegö Type Inequalities for New Classes of Bi-Starlike and Bi-Convex Functions

Abstract: In this paper, we define certain families SE*(ϑ) and CE(ϑ) of holomorphic and bi-univalent functions which are defined in the open unit disk U. We establish upper bounds for the initial Taylor–Maclaurin coefficients and Fekete–Szegö type inequalities for functions in these families.

Cited by 6 publications

References 22 publications

On a Fekete–Szegö Problem Associated with Generalized Telephone Numbers

On a Fekete–Szegö Problem Associated with Generalized Telephone Numbers

New Applications of Fractional q-Calculus Operator for a New Subclass of q-Starlike Functions Related with the Cardioid Domain

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

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