D. Vamshee Krishna (corresponding author), Department of Mathematics, Institut of Technology, GITAM University Visakhapatnam, 530045 Andhra Pradesh, India, e-mail: vamsheekrishna1972@gmail.com; T. Ramreddy, Department of Mathematics, Vidyaranyapuri, Kakatiya University, Warangal, 506009 Andhra Pradesh, India, e-mail: reddytr2@yahoo.com
Abstract: The objective of this paper is to obtain sharp upper bound for the function $f$ for the second Hankel determinant $|a_2a_4-a_3^2|$, 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 $|t_2t_4-t_3^2|$, was determined when it belongs to the same class of functions, using Toeplitz determinants.
Keywords: analytic function; upper bound; second Hankel functional; positive real function; Toeplitz determinant
Classification (MSC 2010): 30C45, 30C50
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