On a subclass of tilted starlike functions with respect to conjugate points / Nur Hazwani Aqilah Abdul Wahid

This thesis is concerned with the function / defined on an open unit disk E = {z : |z| < l} of the complex plane. Let As be the class o f analytic functions defined on E which is normalized and has the Taylor series representation of the form oe f ( z ) = z + a2z 2 + ciyZ* H----- b anz" 4— =...

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Main Author:	Abdul Wahid, Nur Hazwani Aqilah
Format:	Thesis
Language:	English
Published:	2015
Subjects:	Elementary mathematics Arithmetic Analytical methods used in the solution of physical problems
Online Access:	https://ir.uitm.edu.my/id/eprint/15892/1/TM_NUR%20HAZWANI%20AQILAH%20ABDUL%20WAHID%20CS%2015_5.PDF
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spelling	my-uitm-ir.158922022-03-10T01:51:40Z On a subclass of tilted starlike functions with respect to conjugate points / Nur Hazwani Aqilah Abdul Wahid 2015 Abdul Wahid, Nur Hazwani Aqilah Elementary mathematics. Arithmetic Analytical methods used in the solution of physical problems This thesis is concerned with the function / defined on an open unit disk E = {z : \|z\| < l} of the complex plane. Let As be the class o f analytic functions defined on E which is normalized and has the Taylor series representation of the form oe f ( z ) = z + a2z 2 + ciyZ* H----- b anz" 4— = z + ^ anz ". Let H be the class of functions 11=2 co which are analytic and univalent in E of the form co(z)=txz + t2z 2 h— + tnz" h— = ^ t nz". We define the class S ’(a ,S ,A ,B ) for «= 1 which functions in the class S ' (a, S, A,B) satisfy the condition f ia zf'(z) . . ^ 1 1 + Aco(z) /x /(z)+ f(z ) e .— 8 - 1 sin a -----= ---------- 7- - , cog H where g\z) - - — and V J L , 1 + Bco(z) 2 I I 71 tm = c o s a - S with \|ar\| < —, cos« > <*>, 0 < S < 1 and - \< B < A < \ . Some of the basic properties are obtained for the class S '(a ,S ,A , B) such as distortion theorem, z f ' ( z ) growth theorem, argument of -—7—^. and coefficient bounds. The upper and lower g{z ) zf'(z) z f ' i2) bounds of Re—— and Im ■: .r~ for functions in the class S (a,S ,A,B) are also g \z ) g\z) given. This thesis also discusses on the radius problems which are the radius of convexity and the radius of starlikeness for the defined class. Lastly, the coefficient inequalities problems which are the upper bounds for the Second Hankel determinant a2aA- a ^ \| and Fekete-Szego functional a3 - /w , 2 are determined for functions in the class S ’(a,S,A, B). Also included the coefficient determinant with Fekete-Szego parameter which is la,a, - f i a \ 2015 Thesis https://ir.uitm.edu.my/id/eprint/15892/ https://ir.uitm.edu.my/id/eprint/15892/1/TM_NUR%20HAZWANI%20AQILAH%20ABDUL%20WAHID%20CS%2015_5.PDF text en public mphil masters Universiti Teknologi MARA Faculty of Computer and Mathematical Sciences
institution	Universiti Teknologi MARA
collection	UiTM Institutional Repository
language	English
topic	Elementary mathematics Arithmetic Analytical methods used in the solution of physical problems
spellingShingle	Elementary mathematics Arithmetic Analytical methods used in the solution of physical problems Abdul Wahid, Nur Hazwani Aqilah On a subclass of tilted starlike functions with respect to conjugate points / Nur Hazwani Aqilah Abdul Wahid
description	This thesis is concerned with the function / defined on an open unit disk E = {z : \|z\| < l} of the complex plane. Let As be the class o f analytic functions defined on E which is normalized and has the Taylor series representation of the form oe f ( z ) = z + a2z 2 + ciyZ* H----- b anz" 4— = z + ^ anz ". Let H be the class of functions 11=2 co which are analytic and univalent in E of the form co(z)=txz + t2z 2 h— + tnz" h— = ^ t nz". We define the class S ’(a ,S ,A ,B ) for «= 1 which functions in the class S ' (a, S, A,B) satisfy the condition f ia zf'(z) . . ^ 1 1 + Aco(z) /x /(z)+ f(z ) e .— 8 - 1 sin a -----= ---------- 7- - , cog H where g\z) - - — and V J L , 1 + Bco(z) 2 I I 71 tm = c o s a - S with \|ar\| < —, cos« > <*>, 0 < S < 1 and - \< B < A < \ . Some of the basic properties are obtained for the class S '(a ,S ,A , B) such as distortion theorem, z f ' ( z ) growth theorem, argument of -—7—^. and coefficient bounds. The upper and lower g{z ) zf'(z) z f ' i2) bounds of Re—— and Im ■: .r~ for functions in the class S (a,S ,A,B) are also g \z ) g\z) given. This thesis also discusses on the radius problems which are the radius of convexity and the radius of starlikeness for the defined class. Lastly, the coefficient inequalities problems which are the upper bounds for the Second Hankel determinant a2aA- a ^ \| and Fekete-Szego functional a3 - /w , 2 are determined for functions in the class S ’(a,S,A, B). Also included the coefficient determinant with Fekete-Szego parameter which is la,a, - f i a \
format	Thesis
qualification_name	Master of Philosophy (M.Phil.)
qualification_level	Master's degree
author	Abdul Wahid, Nur Hazwani Aqilah
author_facet	Abdul Wahid, Nur Hazwani Aqilah
author_sort	Abdul Wahid, Nur Hazwani Aqilah
title	On a subclass of tilted starlike functions with respect to conjugate points / Nur Hazwani Aqilah Abdul Wahid
title_short	On a subclass of tilted starlike functions with respect to conjugate points / Nur Hazwani Aqilah Abdul Wahid
title_full	On a subclass of tilted starlike functions with respect to conjugate points / Nur Hazwani Aqilah Abdul Wahid
title_fullStr	On a subclass of tilted starlike functions with respect to conjugate points / Nur Hazwani Aqilah Abdul Wahid
title_full_unstemmed	On a subclass of tilted starlike functions with respect to conjugate points / Nur Hazwani Aqilah Abdul Wahid
title_sort	on a subclass of tilted starlike functions with respect to conjugate points / nur hazwani aqilah abdul wahid
granting_institution	Universiti Teknologi MARA
granting_department	Faculty of Computer and Mathematical Sciences
publishDate	2015
url	https://ir.uitm.edu.my/id/eprint/15892/1/TM_NUR%20HAZWANI%20AQILAH%20ABDUL%20WAHID%20CS%2015_5.PDF
_version_	1783733462591602688

On a subclass of tilted starlike functions with respect to conjugate points / Nur Hazwani Aqilah Abdul Wahid

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