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The study of coefficient estimates and Fekete-Szego inequalities for the new classes of m-fold symmetric bi-univalent functions defined using an operator

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SPRINGER
DOI: 10.1186/s13660-023-02920-6

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Analytic functions; Bi-univalent functions; Fekete-Szego functional; m-fold symmetric; Coefficient estimates; Coefficient bounds

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This paper introduces new classes of m-fold symmetric bi-univalent functions and discusses estimates on the Taylor-Maclaurin coefficients |a(m+1)| and |a(2m+1)|. The Fekete-Szego problem for the new classes of functions is also considered. The study incorporates aspects of quantum calculus to enhance novelty and obtain more interesting results.
The objective of this paper is to introduce new classes of m-fold symmetric bi-univalent functions. We discuss estimates on the Taylor-Maclaurin coefficients |a(m+1)| and |a(2m+1)|, and the Fekete-Szego problem is also considered for the new classes of functions introduced. We denote these classes by MF - S-Sigma,m(p,q)(h), MF - S-Sigma,m(p,q)(s), and MF -S-Sigma,m(b,d). Quantum calculus aspects are also considered in this study to enhance its novelty and to obtain more interesting results.

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