Geodesic
Coefficient bounds for regular and bi-univalent functions linked with Gegenbauer polynomials
Problemy analiza, Tome 11 (2022) no. 1, pp. 133-144

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The main goal of the paper is to initiate and explore two sets of regular and bi-univalent (or bi-Schlicht) functions in $\mathfrak{D} =\{z\in\mathbb{C}:|z| 1\}$ 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.
Keywords: Fekete-Szegö, functional, regular function, bi-univalent function, Gegenbauer polynomials. 
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     author = {S. R. Swamy and S. Yal\c{c}{\i}n},
     title = {Coefficient bounds for regular and bi-univalent functions linked with {Gegenbauer} polynomials},
     journal = {Problemy analiza},
     pages = {133--144},
     publisher = {mathdoc},
     volume = {11},
     number = {1},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2022_11_1_a9/}
}
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S. R. Swamy; S. Yalçın. Coefficient bounds for regular and bi-univalent functions linked with Gegenbauer polynomials. Problemy analiza, Tome 11 (2022) no. 1, pp. 133-144. http://geodesic.mathdoc.fr/item/PA_2022_11_1_a9/