Coefficient Estimates and the Fekete–Szegö Problem for New Classes of m-Fold Symmetric Bi-Univalent Functions

Abstract

The results presented in this paper deal with the classical but still prevalent problem of introducing new classes of m-fold symmetric bi-univalent functions and studying properties related to coefficient estimates. Quantum calculus aspects are also considered in this study in order to enhance its novelty and to obtain more interesting results. We present three new classes of bi-univalent functions, generalizing certain previously studied classes. The relation between the known results and the new ones presented here is highlighted. Estimates on the Taylor–Maclaurin coefficients |am+1| and |a2m+1| are obtained and, furthermore, the much investigated aspect of Fekete–Szegő functional is also considered for each of the new classes.

Properties of a Subclass of Analytic Functions Defined by Using an Atangana–Baleanu Fractional Integral Operator

“…This operator was previously used for obtaining differential subordination and fuzzy differential subordination results, and it is used now for introducing and studying a new subclass of functions given in Definition 4. The interesting coefficient estimates obtained in Section 3 of this paper regarding functions from this class could inspire future investigations for studying the Fekete-Szegö problem related to this class, as seen in some very recent papers, [26,27] or a certain order Hankel determinant as done in [28,29]. In Section 4, distortion properties are obtained for the functions from this class and for the derivatives which, connected to the results regarding starlikeness, convexity, and close-to-convexity shown in Section 7, could inspire future studies concerning the geometrical properties of the new subclass of functions.…”

Analitik Fonksiyonların Belirli Bir Sınıfı İçin Fekete-Szegö Problemi Üzerine

“…Very recently, the Fekete-Szegö problem for the subclass of bi-univalent functions with a shell-shaped region was studied by Mustafa and Mrugusundaramoorthy in (Mustafa and Murugusundaramoorthy, 2014) and associated with a nephroid domain in (Srivastava and et al, 2022). Also, the Fekete-Szegö problem is investigated for subclasses of biunivalent functions with respect to the symmetric points defined by Bernoulli polynomials in (Buyankara and et al, 2022), for bi-univalent functions related to the Legendre polynomials in (Cheng and et al, 2022), for m-fold symmetric bi-univalent functions in (Oros and Cotîrlă, 2022).…”

Bi-Univalent Function Classes Defined by Using an Einstein Function and a New Generalised Operator

“…Other typical instances of functions in S such as z − z 2 2 , and z 1−z 2 , do not belong to . For references to related works on bi-univalent functions, see the revival paper by Srivastava et al (2010) , as well as several other studies (Ali et al, 2012;Oros and Cotîrlă, 2022;Srivastava et al, 2018).…”