Coefficient Bounds for a Family of s-Fold Symmetric Bi-Univalent Functions

Author:

Al-shbeil Isra1ORCID,Khan Nazar2ORCID,Tchier Fairouz3ORCID,Xin Qin4ORCID,Malik Sarfraz Nawaz5ORCID,Khan Shahid2ORCID

Affiliation:

1. Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan

2. Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22500, Pakistan

3. Mathematics Department, College of Science, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi Arabia

4. Faculty of Science and Technology, University of the Faroe Islands, Vestarabryggja 15, FO 100 Torshavn, Faroe Islands, Denmark

5. Department of Mathematics, COMSATS University Islamabad, Wah Campus, Wah Cantt 47040, Pakistan

Abstract

We present a new family of s-fold symmetrical bi-univalent functions in the open unit disc in this work. We provide estimates for the first two Taylor–Maclaurin series coefficients for these functions. Furthermore, we define the Salagean differential operator and discuss various applications of our main findings using it. A few new and well-known corollaries are studied in order to show the connection between recent and earlier work.

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Reference54 articles.

1. Certain subclasses of analytic and bi-univalent functions;Srivastava;Appl. Math. Lett.,2010

2. On a coefficient problem for bi-univalent functions;Lewin;Proc. Am. Math. Soc.,1967

3. Brannan, D.A., and Clunie, J.G. (1980). Proceedings of the NATO Advanced Study Institute Held at the University of Durham, Academic Press.

4. The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in |z| < 1;Netanyahu;Arch. Ration. Mech. Anal.,1969

5. Coefficient estimates for bi-univalent functions;Tan;Chin. Ann. Math. Ser. A,1984

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