| Title:
|
Coefficient inequality for a function whose derivative has a positive real part of order $\alpha $ (English) |
| Author:
|
Krishna, Deekonda Vamshee |
| Author:
|
Ramreddy, Thoutreddy |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
140 |
| Issue:
|
1 |
| Year:
|
2015 |
| Pages:
|
43-52 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
analytic function |
| Keyword:
|
upper bound |
| Keyword:
|
second Hankel functional |
| Keyword:
|
positive real function |
| Keyword:
|
Toeplitz determinant |
| MSC:
|
30C45 |
| MSC:
|
30C50 |
| idZBL:
|
Zbl 06433697 |
| idMR:
|
MR3324418 |
| DOI:
|
10.21136/MB.2015.144178 |
| . |
| Date available:
|
2015-03-09T17:39:30Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144178 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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