Differential subordination and coefficients problems of certain analytic functions
| dc.contributor.author | Supramaniam, Shamani | |
| dc.date.accessioned | 2015-05-27T08:18:33Z | |
| dc.date.available | 2015-05-27T08:18:33Z | |
| dc.date.issued | 2014-09 | |
| dc.description.abstract | Let A be the class of normalized analytic functions f on the unit disk D, in the form f(z) = z+ P1n =2 anzn: A function f in A is univalent if it is a one-to-one mapping. This thesis discussed ¯ve research problems. A function f 2 A is said to be bi-univalent in D if both f and its inverse f¡1 are univalent in D. Estimates on the initial coe±cients, ja2j and ja3j, of bi-univalent functions f are investigated when f and f¡1 respectively belong to some subclasses of univalent functions. Next, the bounds for the second Hankel determinant H2(2) = a2a4 ¡ a23 of analytic function f for which zf0(z)=f(z) and 1 + zf00(z)=f0(z) is subordinate to certain analytic function are obtained. Motivated by the earlier work on second order di®erential subordination for analytic functions with ¯xed initial coe±cient, the su±cient conditions for star- likeness and univalence for a subclass of functions with ¯xed second coe±cient are obtained. Then, without ¯xing the second coe±cient, the su±cient condition for convexity of these functions satisfying certain second order and third order di®erential inequalities are determined. Lastly, the close-to-convexity and starlikeness of a subclass of multivalent func- tions are investigated. A few aspects of problems in univalent function theory is discussed in this thesis and some interesting results are obtained. | en_US |
| dc.identifier.uri | http://hdl.handle.net/123456789/777 | |
| dc.subject | Subordination | en_US |
| dc.subject | Coefficient | en_US |
| dc.title | Differential subordination and coefficients problems of certain analytic functions | en_US |
| dc.type | Thesis | en_US |
Files
License bundle
1 - 1 of 1
Loading...
- Name:
- license.txt
- Size:
- 1.71 KB
- Format:
- Item-specific license agreed upon to submission
- Description: