A Family of Holomorphic and m-Fold Symmetric Bi-Univalent Functions Endowed with Coefficient Estimate Problems

Pishtiwan Othman Sabir; Hari Mohan Srivastava; Waggas Galib Atshan; Pshtiwan Othman Mohammed; Nejmeddine Chorfi; Miguel Vivas-Cortez

doi:10.3390/math11183970

A Family of Holomorphic and m-Fold Symmetric Bi-Univalent Functions Endowed with Coefficient Estimate Problems

Pishtiwan Othman Sabir, Hari Mohan Srivastava^*, Waggas Galib Atshan, Pshtiwan Othman Mohammed^*, Nejmeddine Chorfi, Miguel Vivas-Cortez^*

^*Corresponding author for this work

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

7 Scopus citations

Abstract

This paper presents a new general subfamily (Formula presented.) of the family (Formula presented.) that contains holomorphic normalized m-fold symmetric bi-univalent functions in the open unit disk (Formula presented.) associated with the Ruscheweyh derivative operator. For functions belonging to the family introduced here, we find estimates of the Taylor–Maclaurin coefficients (Formula presented.) and (Formula presented.), and the consequences of the results are discussed. The current findings both extend and enhance certain recent studies in this field, and in specific scenarios, they also establish several connections with known results.

Original language	English
Article number	3970
Journal	Mathematics
Volume	11
Issue number	18
DOIs	https://doi.org/10.3390/math11183970
State	Published - Sep 2023

Bibliographical note

Publisher Copyright:
© 2023 by the authors.

Funding

Not applicable.

Keywords

Ruscheweyh derivative operator
bi-convex functions
bi-starlike functions
holomorphic functions
m-fold symmetric bi-univalent functions
univalent functions

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10.3390/math11183970

Cite this

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title = "A Family of Holomorphic and m-Fold Symmetric Bi-Univalent Functions Endowed with Coefficient Estimate Problems",

abstract = "This paper presents a new general subfamily (Formula presented.) of the family (Formula presented.) that contains holomorphic normalized m-fold symmetric bi-univalent functions in the open unit disk (Formula presented.) associated with the Ruscheweyh derivative operator. For functions belonging to the family introduced here, we find estimates of the Taylor–Maclaurin coefficients (Formula presented.) and (Formula presented.), and the consequences of the results are discussed. The current findings both extend and enhance certain recent studies in this field, and in specific scenarios, they also establish several connections with known results.",

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author = "Sabir, {Pishtiwan Othman} and Srivastava, {Hari Mohan} and Atshan, {Waggas Galib} and Mohammed, {Pshtiwan Othman} and Nejmeddine Chorfi and Miguel Vivas-Cortez",

note = "Publisher Copyright: {\textcopyright} 2023 by the authors.",

year = "2023",

month = sep,

doi = "10.3390/math11183970",

language = "English",

volume = "11",

journal = "Mathematics",

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T1 - A Family of Holomorphic and m-Fold Symmetric Bi-Univalent Functions Endowed with Coefficient Estimate Problems

AU - Sabir, Pishtiwan Othman

AU - Srivastava, Hari Mohan

AU - Atshan, Waggas Galib

AU - Mohammed, Pshtiwan Othman

AU - Chorfi, Nejmeddine

AU - Vivas-Cortez, Miguel

PY - 2023/9

Y1 - 2023/9

N2 - This paper presents a new general subfamily (Formula presented.) of the family (Formula presented.) that contains holomorphic normalized m-fold symmetric bi-univalent functions in the open unit disk (Formula presented.) associated with the Ruscheweyh derivative operator. For functions belonging to the family introduced here, we find estimates of the Taylor–Maclaurin coefficients (Formula presented.) and (Formula presented.), and the consequences of the results are discussed. The current findings both extend and enhance certain recent studies in this field, and in specific scenarios, they also establish several connections with known results.

AB - This paper presents a new general subfamily (Formula presented.) of the family (Formula presented.) that contains holomorphic normalized m-fold symmetric bi-univalent functions in the open unit disk (Formula presented.) associated with the Ruscheweyh derivative operator. For functions belonging to the family introduced here, we find estimates of the Taylor–Maclaurin coefficients (Formula presented.) and (Formula presented.), and the consequences of the results are discussed. The current findings both extend and enhance certain recent studies in this field, and in specific scenarios, they also establish several connections with known results.

KW - Ruscheweyh derivative operator

KW - bi-convex functions

KW - bi-starlike functions

KW - holomorphic functions

KW - m-fold symmetric bi-univalent functions

KW - univalent functions

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U2 - 10.3390/math11183970

DO - 10.3390/math11183970

M3 - Article

AN - SCOPUS:85175316553

SN - 2227-7390

VL - 11

JO - Mathematics

JF - Mathematics

IS - 18

M1 - 3970

ER -

A Family of Holomorphic and m-Fold Symmetric Bi-Univalent Functions Endowed with Coefficient Estimate Problems

Abstract

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Keywords

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