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Certain Subclasses of Univalent Functions Linked with q-Chebyshev Polynomial

Timilehin Gideon Shaba, Dere Zainab Olabisi

Abstract: The solutions provided in this work address the classic but still relevant topic of establishing new classes of univalent functions linked to $q$-Chebyshev polynomials and examining coefficient estimates features. Aspects of quantum calculus are also considered in this research to make it more unique and produce more pleasing outcomes. We introduce new classes of univalent functions connected to $q$-Chebyshev polynomials, which generalize certain previously investigated classes. The link among the previously published findings and the current ones are noted. For each of the new classes, estimates for the Taylor-Maclaurin coefficients $|r_2|$ and $|r_3|$ are derived and the much-studied Fekete-Szegö functional.
Keywords: Chebyshev polynomials / univalent functions / Szegö / Subclasses / pleasing / Taylor

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