CERTAIN CLASSES OF BI-UNIVALENT FUNCTIONS OF
COMPLEX ORDER ASSOCIATED WITH QUASI-SUBORDINATION INVOLVING (p, q) -DERIVATIVE OPERATOR

Altınkaya, Şahsene; Yalçın, Sibel

doi:10.46793/kgjmat2004.639a

Cited by 2 publications

(1 citation statement)

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“…Quite a number of mathematicians https://www.indjst.org/ studied the concepts of (p,q)-derivative. For details on (p,q)-calculus one can refer (12)(13)(14)(15) . For the convenience, we provide some basic definitions and concept details of (p,q)-calculus which are used in this paper.…”

Section: Introductionmentioning

confidence: 99%

On New Subclasses of Analytic Functions Involving (p,q)-Derivatives

Shilpa¹

2022

IJST

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Objective:The objectives of the present study are to introduce some new subclasses of analytic functions involving (p,q)-derivatives by using subordination. We derive Fekete-Szegö inequalities for the functions belonging to the new subclasses. Method: Using the concept of (p,q)-derivative of a function and the subordination principle between analytic functions we introduce and study new subclasses. Findings: The Fekete-Szegö problem may be considered as one of the most important results about univalent functions. It was introduced by Fekete-Szegö in 1933. Coefficient estimates for the second and third coefficients of functions belonging to class of analytic functions with specific geometric properties were obtained. We obtain the Fekete-Szegö inequalities for functions belonging to the new subclasses. Moreover, some special cases of the established results are discussed. Novelty: The results of the paper are new and significantly contribute to the existing literature on the topic.

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Section: Introductionmentioning

confidence: 99%

On New Subclasses of Analytic Functions Involving (p,q)-Derivatives

Shilpa¹

2022

IJST

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Two Families of Bi-Univalent Functions Associating the (p, q)-Derivative with Generalized Bivariate Fibonacci Polynomials

Swamy,

Frasin,

Breaz

et al. 2024

Mathematics

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Making use of generalized bivariate Fibonacci polynomials, we propose two families of regular functions of the type ϕ(ζ)=ζ+∑j=2∞djζj, which are bi-univalent in the disc {ζ∈C:|ζ|<1} involving the (p, q)-derivative operator. We find estimates on the coefficients |d2|, |d3| and the of Fekete–Szegö functional for members of these families. Relevant connections to the existing results and new consequences of the main result are presented.

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CERTAIN CLASSES OF BI-UNIVALENT FUNCTIONS OF COMPLEX ORDER ASSOCIATED WITH QUASI-SUBORDINATION INVOLVING (p, q) -DERIVATIVE OPERATOR

Cited by 2 publications

References 20 publications

On New Subclasses of Analytic Functions Involving (p,q)-Derivatives

On New Subclasses of Analytic Functions Involving (p,q)-Derivatives

Two Families of Bi-Univalent Functions Associating the (p, q)-Derivative with Generalized Bivariate Fibonacci Polynomials

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