A family of Analytic Functions Subordinate to Horadam Polynomials
DOI:
https://doi.org/10.29020/nybg.ejpam.v17i1.5022Keywords:
Analytic Functions; Taylor-Maclaurin Series; Principle of Subordination; Horadam Polynomials; Chebyshev polynomials; Coefficient estimates; Fekete-Szeg\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.
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