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ON FEKETE-SZEGÖ INEQUALITY FOR A CLASS OF ANALYTIC FUNCTIONS SATISFYING SUBORDINATE CONDITION ASSOCIATED WITH GEGENBAUER POLYNOMIALS
Keywords:
analytic function, Salagean operator, coefficient estimates, Fekete-Szegö inequality, Gegenbauer polynomials, Chebyshev polynomials, Legendre polynomialsDOI:
https://doi.org/10.17654/0972087125038Abstract
We define a class of analytic functions, $A\left(r, s, \beta, C_n^{(\lambda)}(t)\right)$, satisfying the following condition:
$$
\frac{D_\beta^{r+s}(z)}{D_\beta^r f(z)} \prec H\left(z, C_n^{(\lambda)}(t)\right)
$$
where $\beta \geq 0, r, s \in \mathrm{~N}^*=\mathrm{N} \cup\{0\}, t \in\left(\frac{1}{2}, 1\right]$ and $z \in \Omega$. Besides estimating the coefficients $\left|a_2\right|$ and $\left|a_3\right|$ of a function in this class, we examine the Fekete-Szegö inequality for such a function.
Received: August 26, 2025
Revised: September 6, 2025
Accepted: September 16, 2025
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