Coefficient inequality for a function whose derivative has a positive real part of order $\alpha $

Krishna, Deekonda Vamshee; Ramreddy, Thoutreddy

doi:10.21136/MB.2015.144178

Geodesic

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Coefficient inequality for a function whose derivative has a positive real part of order

α

Krishna, Deekonda Vamshee ; Ramreddy, Thoutreddy

Mathematica Bohemica, Tome 140 (2015) no. 1, pp. 43-52.

Voir la notice de l'article dans Czech Digital Mathematics Library

Résumé

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

α

(0 \leq α 1)

, denoted by

R T (α)

. 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.

MR Zbl

DOI : 10.21136/MB.2015.144178

Classification : 30C45, 30C50
Mots-clés : analytic function; upper bound; second Hankel functional; positive real function; Toeplitz determinant

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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. https://geodesic-test.mathdoc.fr/articles/10.21136/MB.2015.144178/

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