A Class of Analytic Functions with Missing Coefficients
Let 𝑇𝑛(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+1𝑎𝑘𝑧𝑘(𝑛∈𝑁={1,2,3,…}), which are analytic in the open unit disk 𝑈 and satisfy the following subordination condition 𝑓(𝑧)+𝛼𝑧𝑓(𝑧)≺((1+𝐴𝑧)/(1+𝐵𝑧))𝛾, for(𝑧∈𝑈;𝐴≤1;0<𝛾<1),(...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/456729 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | Let 𝑇𝑛(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+1𝑎𝑘𝑧𝑘(𝑛∈𝑁={1,2,3,…}),
which are analytic in the open unit disk 𝑈 and satisfy
the following subordination condition 𝑓(𝑧)+𝛼𝑧𝑓(𝑧)≺((1+𝐴𝑧)/(1+𝐵𝑧))𝛾, for(𝑧∈𝑈;𝐴≤1;0<𝛾<1),(1+𝐴𝑧)/(1+𝐵𝑧), for(𝑧∈𝑈;𝛾=1). We obtain sharp bounds on Re𝑓(𝑧),Re𝑓(𝑧)/𝑧,|𝑓(𝑧)|,
and coefficient estimates for functions
𝑓(𝑧)
belonging to the class
𝑇𝑛(𝐴,𝐵,𝛾,𝛼).
Conditions for univalency and starlikeness, convolution properties, and the radius of convexity
are also considered. |
|---|---|
| ISSN: | 1085-3375 1687-0409 |