Some properties for certain class of bi-univalent functions defined by $ q $-Cătaş operator with bounded boundary rotation

Madian, S. M.

doi:10.3934/math.2022053

Cited by 3 publications

(2 citation statements)

References 41 publications

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“…If both F and F −1 are univalent in D, then F A  is called bi-univalent in D and the class of these functions is denoted by σ. For there are many studies in this class [1][2][3][4][5][6] .…”

Section: Introductionmentioning

confidence: 99%

Faber polynomials estimates for bi-univalent functions of complex order involving q-derivative

Saleh,

Mostafa,

Madian

2023

Math. Syst. Sci.

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In this paper, we define a new subclass of bi-univalent functions of complex order which is defined by subordination in the open unit disc D by using operator. Furthermore, using the Faber polynomial expansions, we get upper bounds for the coefficients of function belonging to this class. It is known that the calculus without the notion of limits is called q-calculus which has influenced many scientific fields due to its important applications. The generalization of derivative in q-calculus that is q-derivative was defined and studied by Jackson. A function is said to be bi-univalent in D if both F and F−1 are univalent in D. The class consisting of bi-univalent functions is denoted by σ. The Faber polynomials play an important role in various areas of mathematical sciences, especially in geometric function theory. The purpose of our study is to obtain bounds for the general coefficients by using Faber polynomial expansion under certain conditions for analytic bi-univalent functions in subclass and also, we obtain improvements on the bounds for the first two coefficients and of functions in this subclass. In certain cases, our estimates improve some of those existing coefficient bounds.

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Section: Introductionmentioning

confidence: 99%

Faber polynomials estimates for bi-univalent functions of complex order involving q-derivative

Saleh,

Mostafa,

Madian

2023

Math. Syst. Sci.

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show abstract

Section: Introductionmentioning

confidence: 99%

Untitled

2023

Math. Syst. Sci.

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In this paper, we define a new subclass of bi-univalent functions of complex order ∑ (휏, 휁; 휑) which is defined by subordination in the open unit disc D by using 훻 퐹(휗) operator. Furthermore, using the Faber polynomial expansions, we get upper bounds for the coefficients of function belonging to this class. It is known that the calculus without the notion of limits is called q-calculus which has influenced many scientific fields due to its important applications. The generalization of derivative in q-calculus that is q-derivative was defined and studied by Jackson. A function 퐹 ∈ 퐴 is said to be bi-univalent in D if both F and F −1 are univalent in D. The class consisting of bi-univalent functions is denoted by σ. The Faber polynomials play an important role in various areas of mathematical sciences, especially in geometric function theory. The purpose of our study is to obtain bounds for the general coefficients |푎 |(푛 ≥ 3) by using Faber polynomial expansion under certain conditions for analytic bi-univalent functions in subclass ∑ (휏, 휁; 휙) and also, we obtain improvements on the bounds for the first two coefficients |푎 | and |푎 | of functions in this subclass. In certain cases, our estimates improve some of those existing coefficient bounds.

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Fekete–Szegö inequalities on certain subclasses of analytic functions defined by $$\lambda$$-pseudo-q-difference operator associated with s-sigmoid function

Olatunji

2022

Bol. Soc. Mat. Mex.

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Some properties for certain class of bi-univalent functions defined by $ q $-Cătaş operator with bounded boundary rotation

Cited by 3 publications

References 41 publications

Faber polynomials estimates for bi-univalent functions of complex order involving q-derivative

Faber polynomials estimates for bi-univalent functions of complex order involving q-derivative

Untitled

Fekete–Szegö inequalities on certain subclasses of analytic functions defined by $$\lambda$$-pseudo-q-difference operator associated with s-sigmoid function

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