Applications of First-Order Differential Subordination for Subfamilies of Analytic Functions Related to Symmetric Image Domains

Khan, Muhammad Ghaffar; Khan, Bilal; Gong, Jianhua; Tchier, Fairouz; Tawfiq, Ferdous M. O.

doi:10.3390/sym15112004

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A Set Of Lemmas1

Introduction1

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2023

2024

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Cited by 4 publications

(2 citation statements)

References 15 publications

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“…The subsequent Lemmas 1-4 will help to demonstrate our main findings, where c t , c t+k , and c t+2k for t, k ∈ N are coefficients of the Taylor series (6).…”

Section: A Set Of Lemmasmentioning

confidence: 71%

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Analytic Functions Related to a Balloon-Shaped Domain

Ahmad,

Gong,

Al-Shbeil

et al. 2023

Fractal Fract

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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 X defined in the new domain, including the sharp estimates for the coefficients a2,a3, and a4, and for three second-order and third-order Hankel determinants, H2,1X,H2,2X, and H3,1X. The optimality of each obtained estimate is given as well.

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“…The subsequent Lemmas 1-4 will help to demonstrate our main findings, where c t , c t+k , and c t+2k for t, k ∈ N are coefficients of the Taylor series (6).…”

Section: A Set Of Lemmasmentioning

confidence: 71%

“…Using the concept of subordination, many subclasses have been defined and studied, such as S * , C, K and R of starlike, convex, close to convex, and functions with bounded turnings, respectively. See [2][3][4][5][6] for the new results about more subclasses.…”

Section: Introductionmentioning

confidence: 99%