Geodesic
Coefficient inequality for a function whose derivative has a positive real part of order $\alpha $
Mathematica Bohemica, Tome 140 (2015) no. 1, pp. 43-52

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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.
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.
DOI : 10.21136/MB.2015.144178
Classification : 30C45, 30C50
Keywords: analytic function; upper bound; second Hankel functional; positive real function; Toeplitz determinant 
Krishna, Deekonda Vamshee; Ramreddy, Thoutreddy. Coefficient inequality for a function whose derivative has a positive real part of order $\alpha $. Mathematica Bohemica, Tome 140 (2015) no. 1, pp. 43-52. doi: 10.21136/MB.2015.144178
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