Properties of tilted univalent analytic functions of order δ / Sidik Rathi
This thesis deals with the functions f9 analytic and univalent in the open unit disk denoted as U = {z e C: Izl < lj. Let A be the class of analytic functions/defined in U and S be the subclass of A normalized by /(o) = 0, / ' ( o ) = 1 and has the Taylor series expansion of the form 00 f(z)...
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| Format: | Thesis |
| Language: | English |
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2015
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| Online Access: | https://ir.uitm.edu.my/id/eprint/15348/2/15348.pdf |
| _version_ | 1825734451378782208 |
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| author | Rathi, Sidik |
| author_facet | Rathi, Sidik |
| author_sort | Rathi, Sidik |
| collection | UITM |
| description | This thesis deals with the functions f9 analytic and univalent in the open unit disk denoted as U = {z e C: Izl < lj. Let A be the class of analytic functions/defined in U and S be the subclass of A normalized by /(o) = 0, / ' ( o ) = 1 and has the Taylor series expansion of the form 00 f(z)= z + a2z2 +a3z3 +••• = z+Janzn.
n = 2 Also, let P be the subclass of A consisting functions h9 such that Re{/z(z)} > 0 , h(o) = 1 and has the form of 00 h(z) = \ + hxz + h2z2 +••- = !+2_\KZ"< n = \ In this thesis, we investigate on the class P{X9S) of A- tilted Caratheodory functions of order 8 and the subclasses of S denoted by C{A9S)of X-close-toconvex functions of order 8 . Such functions in P {X98) and Cg (A,S) satisfies
Re{euh(z)}> 8 and Rejea ^ - ^ 1 > 8 (zeU) respectively with \A\ < — , cos(/l) >8, 0 < 8 < 1 and ga (z) = —f or 0 < a < 1. 2 (l - az)
Some basic properties such as representation function, coefficient bounds, distortion theorem and growth theorem for the class P{A,9S) and Cg {X9 8) = C (X9 8) are obtained. The bounds for real and imaginary part of he P(X98) and / ' e Cg(X98) are also determined. We also discuss on the coefficient inequalities which consist of the upper bounds for the second Hankel determinant, a2a4 -a3 and the Feketeszego functional, jua2 . We determined the upper bound for a2a4 •a. for function in C (A98) and the upper bound for # 3 - / ^ 2 for function in C (Z98).Lastly, we discuss on the radius problems which focuses on finding the radius of convexity and the radius of starlikeness for the class C (A98). |
| first_indexed | 2024-03-06T01:31:57Z |
| format | Thesis |
| id | oai:ir.uitm.edu.my:15348 |
| institution | Universiti Teknologi MARA |
| language | English |
| last_indexed | 2024-03-06T01:31:57Z |
| publishDate | 2015 |
| record_format | dspace |
| spelling | oai:ir.uitm.edu.my:153482022-11-23T03:05:17Z https://ir.uitm.edu.my/id/eprint/15348/ Properties of tilted univalent analytic functions of order δ / Sidik Rathi Rathi, Sidik Study and teaching Analysis This thesis deals with the functions f9 analytic and univalent in the open unit disk denoted as U = {z e C: Izl < lj. Let A be the class of analytic functions/defined in U and S be the subclass of A normalized by /(o) = 0, / ' ( o ) = 1 and has the Taylor series expansion of the form 00 f(z)= z + a2z2 +a3z3 +••• = z+Janzn. n = 2 Also, let P be the subclass of A consisting functions h9 such that Re{/z(z)} > 0 , h(o) = 1 and has the form of 00 h(z) = \ + hxz + h2z2 +••- = !+2_\KZ"< n = \ In this thesis, we investigate on the class P{X9S) of A- tilted Caratheodory functions of order 8 and the subclasses of S denoted by C{A9S)of X-close-toconvex functions of order 8 . Such functions in P {X98) and Cg (A,S) satisfies Re{euh(z)}> 8 and Rejea ^ - ^ 1 > 8 (zeU) respectively with \A\ < — , cos(/l) >8, 0 < 8 < 1 and ga (z) = —f or 0 < a < 1. 2 (l - az) Some basic properties such as representation function, coefficient bounds, distortion theorem and growth theorem for the class P{A,9S) and Cg {X9 8) = C (X9 8) are obtained. The bounds for real and imaginary part of he P(X98) and / ' e Cg(X98) are also determined. We also discuss on the coefficient inequalities which consist of the upper bounds for the second Hankel determinant, a2a4 -a3 and the Feketeszego functional, jua2 . We determined the upper bound for a2a4 •a. for function in C (A98) and the upper bound for # 3 - / ^ 2 for function in C (Z98).Lastly, we discuss on the radius problems which focuses on finding the radius of convexity and the radius of starlikeness for the class C (A98). 2015 Thesis NonPeerReviewed text en https://ir.uitm.edu.my/id/eprint/15348/2/15348.pdf Properties of tilted univalent analytic functions of order δ / Sidik Rathi. (2015) Masters thesis, thesis, Universiti Teknologi MARA (UiTM). |
| spellingShingle | Study and teaching Analysis Rathi, Sidik Properties of tilted univalent analytic functions of order δ / Sidik Rathi |
| title | Properties of tilted univalent analytic functions of order δ / Sidik Rathi |
| title_full | Properties of tilted univalent analytic functions of order δ / Sidik Rathi |
| title_fullStr | Properties of tilted univalent analytic functions of order δ / Sidik Rathi |
| title_full_unstemmed | Properties of tilted univalent analytic functions of order δ / Sidik Rathi |
| title_short | Properties of tilted univalent analytic functions of order δ / Sidik Rathi |
| title_sort | properties of tilted univalent analytic functions of order δ sidik rathi |
| topic | Study and teaching Analysis |
| url | https://ir.uitm.edu.my/id/eprint/15348/2/15348.pdf |
| work_keys_str_mv | AT rathisidik propertiesoftiltedunivalentanalyticfunctionsoforderdsidikrathi |