Abstract and Applied Analysis

A Class of Analytic Functions with Missing Coefficients

Ding-Gong Yang and Jin-Lin Liu

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2011 (2011), Article ID 456729, 16 pages.

Dates
First available in Project Euclid: 12 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1313171208

Digital Object Identifier
doi:10.1155/2011/456729

Mathematical Reviews number (MathSciNet)
MR2576838

Zentralblatt MATH identifier
1220.30028

Citation

Yang, Ding-Gong; Liu, Jin-Lin. A Class of Analytic Functions with Missing Coefficients. Abstr. Appl. Anal. 2011 (2011), Article ID 456729, 16 pages. doi:10.1155/2011/456729. https://projecteuclid.org/euclid.aaa/1313171208


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