The U -Radius And Hankel Determinant For Analytic Functions, And Product Of Logharmonic Mappings
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...
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| Format: | Thesis |
| Language: | en |
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2017
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| Online Access: | http://eprints.usm.my/47548/1/NAJLA%20MOHAMMED%20ALARIFI.pdf%20cut.pdf http://eprints.usm.my/47548/ |
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| _version_ | 1834503887132819456 |
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| author | Mohammed Alarifi, Najla |
| author_facet | Mohammed Alarifi, Najla |
| author_sort | Mohammed Alarifi, Najla |
| building | Hamzah Sendut Library |
| collection | Institutional Repository |
| content_provider | Universiti Sains Malaysia |
| content_source | USM Institutional Repository |
| continent | Asia |
| country | Malaysia |
| description | 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 |
| format | Thesis |
| id | my.usm.eprints.47548 |
| institution | Universiti Sains Malaysia |
| language | en |
| publishDate | 2017 |
| record_format | eprints |
| spelling | my.usm.eprints.47548 http://eprints.usm.my/47548/ The U -Radius And Hankel Determinant For Analytic Functions, And Product Of Logharmonic Mappings Mohammed Alarifi, Najla QA1 Mathematics (General) 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 2017-10 Thesis NonPeerReviewed application/pdf en http://eprints.usm.my/47548/1/NAJLA%20MOHAMMED%20ALARIFI.pdf%20cut.pdf Mohammed Alarifi, Najla (2017) The U -Radius And Hankel Determinant For Analytic Functions, And Product Of Logharmonic Mappings. PhD thesis, Universiti Sains Malaysia. |
| spellingShingle | QA1 Mathematics (General) Mohammed Alarifi, Najla The U -Radius And Hankel Determinant For Analytic Functions, And Product Of Logharmonic Mappings |
| title | The U -Radius And Hankel Determinant For Analytic Functions, And Product Of Logharmonic Mappings |
| title_full | The U -Radius And Hankel Determinant For Analytic Functions, And Product Of Logharmonic Mappings |
| title_fullStr | The U -Radius And Hankel Determinant For Analytic Functions, And Product Of Logharmonic Mappings |
| title_full_unstemmed | The U -Radius And Hankel Determinant For Analytic Functions, And Product Of Logharmonic Mappings |
| title_short | The U -Radius And Hankel Determinant For Analytic Functions, And Product Of Logharmonic Mappings |
| title_sort | u -radius and hankel determinant for analytic functions, and product of logharmonic mappings |
| topic | QA1 Mathematics (General) |
| url | http://eprints.usm.my/47548/1/NAJLA%20MOHAMMED%20ALARIFI.pdf%20cut.pdf http://eprints.usm.my/47548/ |
| url_provider | http://eprints.usm.my/ |