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2011 A Class of Analytic Functions with Missing Coefficients
Ding-Gong Yang, Jin-Lin Liu
Abstr. Appl. Anal. 2011: 1-16 (2011). DOI: 10.1155/2011/456729

Abstract

Let T n ( A , B , γ , α ) ( - 1 B < 1 , B < A , 0 < γ 1 and α > 0 ) denote the class of functions of the form f ( z ) = z + k = n + 1 a k z k ( n N = { 1 , 2 , 3 , } ) , which are analytic in the open unit disk U and satisfy the following subordination condition f ( z ) + α z f ( z ) ( ( 1 + A z ) / ( 1 + B z ) ) γ , for ( z U ; A 1 ; 0 < γ < 1 ) , ( 1 + A z ) / ( 1 + B z ) , for ( z U ; γ = 1 ) . We obtain sharp bounds on R e f ' ( z ) , R e f ( z ) / z , | f ( z ) | , and coefficient estimates for functions f ( z ) belonging to the class T n ( A , B , γ , α ) . Conditions for univalency and starlikeness, convolution properties, and the radius of convexity are also considered.

Citation

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Ding-Gong Yang. Jin-Lin Liu. "A Class of Analytic Functions with Missing Coefficients." Abstr. Appl. Anal. 2011 1 - 16, 2011. https://doi.org/10.1155/2011/456729

Information

Published: 2011
First available in Project Euclid: 12 August 2011

zbMATH: 1220.30028
MathSciNet: MR2576838
Digital Object Identifier: 10.1155/2011/456729

Rights: Copyright © 2011 Hindawi

Vol.2011 • 2011
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