Subordination And Convolution Of Multivalent Functions And Starlikeness Of Integral Transforms

dc.contributor.author	Badghaish, Abeer Omar
dc.date.accessioned	2020-02-24T02:05:31Z
dc.date.available	2020-02-24T02:05:31Z
dc.date.issued	2012-01
dc.description.abstract	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􀀀q Q(z); or zf(q+1)(z) f(q)(z) 􀀀 p + q + 1 Q(z): Here Q is an appropriate superordinate function, (p; q) = p!=(p 􀀀 q)!, and denotes subordination. As important consequences, several criteria for univalence and convexity are obtained for the case p = q = 1: The notion of starlikeness with respect to n􀀀ply points is also generalized to the case of multivalent functions. These are functions f 2 Ap satisfying	en_US
dc.identifier.uri	http://hdl.handle.net/123456789/9549
dc.language.iso	en	en_US
dc.subject	Analytic functions	en_US
dc.title	Subordination And Convolution Of Multivalent Functions And Starlikeness Of Integral Transforms	en_US
dc.type	Thesis	en_US

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