Abstract
The object of this article is to explore two subclasses of regular and bi-univalent functions subordinate to Horadam polynomials in the disk $\{\varsigma\in\mathbb{C}:|\varsigma| <1\}$. We originate upper bounds for the initial Taylor-Maclaurin coefficient estimates of functions in these subclasses. Fekete-Szeg\"o functional problem is also established. Furthermore, we present some new observations and investigate relevant connections to existing results.
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