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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Main Author:	Rathi, Sidik
Format:	Thesis
Language:	English
Published:	2015
Subjects:	Study and teaching Analysis
Online Access:	https://ir.uitm.edu.my/id/eprint/15348/2/15348.pdf
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spelling	my-uitm-ir.153482022-11-23T03:05:17Z Properties of tilted univalent analytic functions of order δ / Sidik Rathi 2015 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 https://ir.uitm.edu.my/id/eprint/15348/ https://ir.uitm.edu.my/id/eprint/15348/2/15348.pdf text en public mphil masters Universiti Teknologi MARA (UiTM) Faculty Computer and Mathematical Sciences
institution	Universiti Teknologi MARA
collection	UiTM Institutional Repository
language	English
topic	Study and teaching Analysis
spellingShingle	Study and teaching Analysis Rathi, Sidik Properties of tilted univalent analytic functions of order δ / Sidik Rathi
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).
format	Thesis
qualification_name	Master of Philosophy (M.Phil.)
qualification_level	Master's degree
author	Rathi, Sidik
author_facet	Rathi, Sidik
author_sort	Rathi, Sidik
title	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_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_sort	properties of tilted univalent analytic functions of order δ / sidik rathi
granting_institution	Universiti Teknologi MARA (UiTM)
granting_department	Faculty Computer and Mathematical Sciences
publishDate	2015
url	https://ir.uitm.edu.my/id/eprint/15348/2/15348.pdf
_version_	1783733375906873344

Properties of tilted univalent analytic functions of order δ / Sidik Rathi

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