Coefficient bounds for regular and bi-univalent functions linked with Gegenbauer polynomials

The main goal of the paper is to initiate and explore two sets of regular and bi-univalent (or bi-Schlicht) functions in 𝔇 = {𝑧 ∈ C : |𝑧| < 1} linked with Gegenbauer polynomials. We investigate certain coefficient bounds for functions in these families. Continuing the study on the initial coeffic...

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Bibliographic Details
Published inIssues of analysis Vol. 29; no. 1; pp. 133 - 144
Main Authors Swamy, S. R., Yalçın, S.
Format Journal Article
LanguageEnglish
Published Petrozavodsk State University 01.02.2022
Subjects
bi-univalent function
fekete-szeg¨o functional
gegenbauer polynomials
regular function
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Summary:The main goal of the paper is to initiate and explore two sets of regular and bi-univalent (or bi-Schlicht) functions in 𝔇 = {𝑧 ∈ C : |𝑧| < 1} linked with Gegenbauer polynomials. We investigate certain coefficient bounds for functions in these families. Continuing the study on the initial coefficients of these families, we obtain the functional of Fekete-Szegö for each of the two families. Furthermore, we present few interesting observations of the results investigated.
ISSN:2306-3432
2306-3424
2306-3432
DOI:10.15393/j3.art.2022.10351