A family of Analytic Functions Subordinate to Horadam Polynomials

Abstract

In this paper, we introduce and investigate a family of analytic functions, denoted by $\mathcal{F}(\Pi, \alpha, \beta, \lambda, \delta, \mu)$, defined by means of Horadam polynomials. For functions in this family, we derive the estimations for the initial Taylor-Maclaurin coefficients $|a_2|$ and $|a_3|$. Moreover, we obtain the classical Fekete-Szeg\"{o} inequality of functions belonging to this family.