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Keywords:
analytic function; upper bound; second Hankel functional; positive real function; Toeplitz determinant
analytic function; upper bound; second Hankel functional; positive real function; Toeplitz determinant
Summary:
The objective of this paper is to obtain sharp upper bound for the function $f$ for the second Hankel determinant $|a_{2}a_{4}-a_{3}^{2}|$, when it belongs to the class of functions whose derivative has a positive real part of order $\alpha $ $(0\leq \alpha <1)$, denoted by $ RT(\alpha )$. Further, an upper bound for the inverse function of $f$ for the nonlinear functional (also called the second Hankel functional), denoted by $|t_{2}t_{4}-t_{3}^{2}|$, was determined when it belongs to the same class of functions, using Toeplitz determinants.
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