Differential Subordination Of Analytic Functions With Fixed Initial Coefficient
| dc.contributor.author | SALLEH, NURSHAMIMI | |
| dc.date.accessioned | 2016-06-09T06:55:16Z | |
| dc.date.available | 2016-06-09T06:55:16Z | |
| dc.date.issued | 2015-10 | |
| dc.description.abstract | This thesis investigates complex-valued analytic functions in the unit disk with fixed initial coefficient or with fixed second coefficient in its series expansion. The methodology of differential subordination is adapted and enhanced to enable its use, which requires obtaining appropriate classes of admissible functions. Three research problems are discussed in this thesis. First, the linear second-order differential subordination A(z)z2p00(z)+B(z)zp0(z)+C(z)p(z)+D(z) h(z); is considered. Conditions on the complex-valued functions A;B;C;D and h are derived to ensure an appropriate differential implication is obtained involving the solutions p. For particular choices of h, these implications are interpreted geometrically. Connections are made with earlier known results. These subordination results are next used to study inclusion properties for linear integral operators on certain subclasses of analytic functions with fixed initial coefficient. Of interest would be the linear integral operator of the form I[ f ](z) = r +g zgf(z) Z z 0 f (t)j(t)tg1 dt; where r and g are complex numbers, and f;j and f belong to some classes of analytic functions. The linear integral operator is shown to map certain subclasses of analytic functions with fixed initial coefficient into itself. The final problem considered is in obtaining sufficient conditions for analytic functions with fixed initial coefficient to be starlike or convex. These conditions are framed in terms of the Schwarzian derivative. | en_US |
| dc.identifier.uri | http://hdl.handle.net/123456789/2078 | |
| dc.subject | Differential Subordination Of Analytic Functions | en_US |
| dc.subject | With Fixed Initial Coefficient | en_US |
| dc.title | Differential Subordination Of Analytic Functions With Fixed Initial Coefficient | en_US |
| dc.type | Thesis | en_US |
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