Subordination And Convolution Of Multivalent Functions And Starlikeness Of Integral Transforms
This thesis deals with analytic functions as well as multivalent functions de- �ned on the unit disk U. In most cases, these functions are assumed to be normalized, either of the form f(z) = z + 1X k=2 akzk; or f(z) = zp + 1X k=1 ak+pzk+p; p a �xed positive integer. Let A be the class of...
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2012
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my.usm.eprints.46312 http://eprints.usm.my/46312/ Subordination And Convolution Of Multivalent Functions And Starlikeness Of Integral Transforms Badghaish, Abeer Omar QA1 Mathematics (General) This thesis deals with analytic functions as well as multivalent functions de- �ned on the unit disk U. In most cases, these functions are assumed to be normalized, either of the form f(z) = z + 1X k=2 akzk; or f(z) = zp + 1X k=1 ak+pzk+p; p a �xed positive integer. Let A be the class of functions f with the �rst normalization, while Ap consists of functions f with the latter normalization. Five research problems are discussed in this work. First, let f(q) denote the q-th derivative of a function f 2 Ap. Using the theory of di�erential subordination, su�cient conditions are obtained for the following di�erential chain to hold: f(q)(z) �(p; q)zp 2012-01 Thesis NonPeerReviewed application/pdf en http://eprints.usm.my/46312/1/ABEER%20OMAR%20BADGHAISH_HJ.pdf Badghaish, Abeer Omar (2012) Subordination And Convolution Of Multivalent Functions And Starlikeness Of Integral Transforms. PhD thesis, Universiti Sains Malaysia. |
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QA1 Mathematics (General) Badghaish, Abeer Omar Subordination And Convolution Of Multivalent Functions And Starlikeness Of Integral Transforms |
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This thesis deals with analytic functions as well as multivalent functions de-
�ned on the unit disk U. In most cases, these functions are assumed to be normalized,
either of the form
f(z) = z +
1X
k=2
akzk;
or
f(z) = zp +
1X
k=1
ak+pzk+p;
p a �xed positive integer. Let A be the class of functions f with the �rst normalization,
while Ap consists of functions f with the latter normalization. Five
research problems are discussed in this work.
First, let f(q) denote the q-th derivative of a function f 2 Ap. Using the theory
of di�erential subordination, su�cient conditions are obtained for the following
di�erential chain to hold:
f(q)(z)
�(p; q)zp |
format |
Thesis |
author |
Badghaish, Abeer Omar |
author_facet |
Badghaish, Abeer Omar |
author_sort |
Badghaish, Abeer Omar |
title |
Subordination And Convolution Of Multivalent Functions And Starlikeness Of Integral Transforms |
title_short |
Subordination And Convolution Of Multivalent Functions And Starlikeness Of Integral Transforms |
title_full |
Subordination And Convolution Of Multivalent Functions And Starlikeness Of Integral Transforms |
title_fullStr |
Subordination And Convolution Of Multivalent Functions And Starlikeness Of Integral Transforms |
title_full_unstemmed |
Subordination And Convolution Of Multivalent Functions And Starlikeness Of Integral Transforms |
title_sort |
subordination and convolution of multivalent functions and starlikeness of integral transforms |
publishDate |
2012 |
url |
http://eprints.usm.my/46312/1/ABEER%20OMAR%20BADGHAISH_HJ.pdf http://eprints.usm.my/46312/ |
_version_ |
1662755767352033280 |
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13.211869 |