Analytic Functions Related to a Balloon-Shaped Domain

Adeel Ahmad; Jianhua Gong; Isra Al-Shbeil; Akhter Rasheed; Asad Ali; Saqib Hussain

doi:10.3390/fractalfract7120865

Analytic Functions Related to a Balloon-Shaped Domain

Adeel Ahmad, Jianhua Gong, Isra Al-Shbeil, Akhter Rasheed, Asad Ali, Saqib Hussain

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

One of the fundamental parts of Geometric Function Theory is the study of analytic functions in different domains with critical geometrical interpretations. This article defines a new generalized domain obtained based on the quotient of two analytic functions. We derive various properties of the new class of normalized analytic functions (Formula presented.) defined in the new domain, including the sharp estimates for the coefficients (Formula presented.), and (Formula presented.), and for three second-order and third-order Hankel determinants, (Formula presented.), and (Formula presented.). The optimality of each obtained estimate is given as well.

Original language	English
Article number	865
Journal	Fractal and Fractional
Volume	7
Issue number	12
DOIs	https://doi.org/10.3390/fractalfract7120865
Publication status	Published - Dec 2023

Keywords

Hankel determinant
analytic function
generalized domain
sharp upper bound
subordination

ASJC Scopus subject areas

Analysis
Statistical and Nonlinear Physics
Statistics and Probability

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10.3390/fractalfract7120865

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abstract = "One of the fundamental parts of Geometric Function Theory is the study of analytic functions in different domains with critical geometrical interpretations. This article defines a new generalized domain obtained based on the quotient of two analytic functions. We derive various properties of the new class of normalized analytic functions (Formula presented.) defined in the new domain, including the sharp estimates for the coefficients (Formula presented.), and (Formula presented.), and for three second-order and third-order Hankel determinants, (Formula presented.), and (Formula presented.). The optimality of each obtained estimate is given as well.",

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T1 - Analytic Functions Related to a Balloon-Shaped Domain

AU - Ahmad, Adeel

AU - Gong, Jianhua

AU - Al-Shbeil, Isra

AU - Rasheed, Akhter

AU - Ali, Asad

AU - Hussain, Saqib

PY - 2023/12

Y1 - 2023/12

N2 - One of the fundamental parts of Geometric Function Theory is the study of analytic functions in different domains with critical geometrical interpretations. This article defines a new generalized domain obtained based on the quotient of two analytic functions. We derive various properties of the new class of normalized analytic functions (Formula presented.) defined in the new domain, including the sharp estimates for the coefficients (Formula presented.), and (Formula presented.), and for three second-order and third-order Hankel determinants, (Formula presented.), and (Formula presented.). The optimality of each obtained estimate is given as well.

AB - One of the fundamental parts of Geometric Function Theory is the study of analytic functions in different domains with critical geometrical interpretations. This article defines a new generalized domain obtained based on the quotient of two analytic functions. We derive various properties of the new class of normalized analytic functions (Formula presented.) defined in the new domain, including the sharp estimates for the coefficients (Formula presented.), and (Formula presented.), and for three second-order and third-order Hankel determinants, (Formula presented.), and (Formula presented.). The optimality of each obtained estimate is given as well.

KW - Hankel determinant

KW - analytic function

KW - generalized domain

KW - sharp upper bound

KW - subordination

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Analytic Functions Related to a Balloon-Shaped Domain

Abstract

Keywords

ASJC Scopus subject areas

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