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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{PA_2022_11_1_a9,
     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/}
}
TY  - JOUR
AU  - S. R. Swamy
AU  - S. Yalçın
TI  - Coefficient bounds for regular and bi-univalent functions linked with Gegenbauer polynomials
JO  - Problemy analiza
PY  - 2022
SP  - 133
EP  - 144
VL  - 11
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PA_2022_11_1_a9/
LA  - en
ID  - PA_2022_11_1_a9
ER  - 
%0 Journal Article
%A S. R. Swamy
%A S. Yalçın
%T Coefficient bounds for regular and bi-univalent functions linked with Gegenbauer polynomials
%J Problemy analiza
%D 2022
%P 133-144
%V 11
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PA_2022_11_1_a9/
%G en
%F PA_2022_11_1_a9
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/

[1] Amourah A., Alamoush A., Al-Kaseasbeh M., “Gegenbauer polynomials and biunivalent functions”, Palestine J. Math., 10:2 (2021), 625–632

[2] Amourah A., Frasin B. A., Abdeljawad T., “Fekete-Szegö inequality for analytic and biunivalent functions subordinate to Gegenbauer polynomials”, J. Funct. Spaces, 2021 (2021), 5574673, 7 pp. | DOI

[3] Brannan D. A., Taha T. S., “On some classes of bi-univalent functions”, Mathematical analysis and its applications (Kuwait), KFAS Proceedings Series, 3, eds. S. M. Mazhar, A. Hamoui, N.S. Faour, Pergamon Press (Elsevier Science Limited), Oxford, 1985, 53–60; 1988; Stud. Univ. Babeş-Bolyai Math., 31:2 (1986), 70–77 | DOI

[4] Brannan D. A., Clunie J. G., “Aspects of contemporary complex analysis”, Proceedings of the NATO Advanced study institute (University of Durhary), Academic press, New York, 1979

[5] Duren P. L., Univalent Functions, Grundlehren der Mathematischen Wissenschaften, 259, Springer-Verlag, New York, 1983

[6] Fekete M., Szegö G., “Eine Bemerkung Über Ungerade Schlichte Funktionen”, J. Lond. Math. Soc., 89 (1933), 85–89 (in German) | DOI

[7] Frasin B. A., Aouf M. K., “New subclasses of bi-univalent functions”, Appl. Math. Lett., 24:9 (2011), 1569–1573 | DOI

[8] Kiepiela K., Naraniecka I., Szynal J., “The Gegenbauer polynomials and typically real functions”, J. Comput. Appl. Math., 153:1–2 (2003), 273–282 | DOI

[9] Lewin M., “On a coefficient problem for bi-univalent functions”, Proc. Amer. Math. Soc., 18:1 (1967), 63–68 | DOI

[10] Srivastava H. M., Mishra A. K., Gochhayat P., “Certain subclasses of analytic and bi-univalent functions”, Appl. Math. Lett., 23:10 (2010), 1188–1192 | DOI

[11] Tan D. L., “Coefficient estimates for bi-univalent functions”, Chinese Ann. Math. Ser. A, 5:5 (1984), 559–568