The U -Radius And Hankel Determinant For Analytic Functions, And Product Of Logharmonic Mappings
| dc.contributor.author | Mohammed Alarifi, Najla | |
| dc.date.accessioned | 2020-10-14T07:54:18Z | |
| dc.date.available | 2020-10-14T07:54:18Z | |
| dc.date.issued | 2017-10 | |
| dc.description.abstract | This thesis studies geometric and analytic properties of complex-valued analytic functions and logharmonic mappings in the open unit disk D. It investigates four research problems. As a precursor to the first, let U be the class consisting of normalized analytic functions f satisfying |(z= f (z))2 f ′(z)−1| < 1: All functions f ∈ U are univalent. In the first problem, the U -radius is determined for several classes of analytic functions. These include the classes of functions f satisfying the inequality Re f (z)=g(z) > 0; or | f (z)=g(z)−1| < 1 in D; for g belonging to a certain class of analytic functions. In most instances, the exact U -radius are found. A recent conjecture by Obradovi´c and Ponnusamy concerning the radius of univalence for a product involving univalent functions is also shown to hold true. The second problem deals with the Hankel determinant of analytic functions. For a normalized analytic function f ; let z f ′(z)= f (z) or 1+z f ′′(z)= f ′(z) be subordinate to a given analytic function φ in D. Further let F be its kth-root transform, that is, F(z) = z[f(zk)=zk]1k | en_US |
| dc.identifier.uri | http://hdl.handle.net/123456789/10445 | |
| dc.language.iso | en | en_US |
| dc.publisher | Universiti Sains Malaysia | en_US |
| dc.subject | The U -Radius And Hankel Determinant | en_US |
| dc.subject | Analytic Functions, And Product Of Logharmonic Mappings | en_US |
| dc.title | The U -Radius And Hankel Determinant For Analytic Functions, And Product Of Logharmonic Mappings | en_US |
| dc.type | Thesis | en_US |
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