Inclusion Properties Of Linear Operators And Analytic Functions
| dc.contributor.author | Moradi Nargesi, Mahnaz | |
| dc.date.accessioned | 2018-12-12T03:09:51Z | |
| dc.date.available | 2018-12-12T03:09:51Z | |
| dc.date.issued | 2013 | |
| dc.description.abstract | This thesis studies the class A of normalized analytic functions in the open unit disk U of the complex plane. The class of meromorphic functions in the punctured unit disk which does not include the origin is also studied. This thesis investigates six research problems. First, the classical subclasses of starlike, convex, close-toconvex and quasi-convex functions are extended by introducing new subclasses of analytic and meromorphic functions. The closure properties of these newly de ned classes are investigated and it is shown that these classes are closed under convolution with prestarlike functions and the Bernardi-Libera-Livingston integral operator. The univalence of functions f(z) = z + P1n=2 anzn 2 A is investigated by requiring the Schwarzian derivative S(f; z) and the second coe cient a2 of f to satisfy certain inequalities. New criterion for analytic functions to be strongly - Bazilevi c of nonnegative order is established in terms of the Schwarzian derivatives and the second coe cients. Also, similar conditions on the second coe cient of f and its Schwarzian derivative S(f; z) are obtained that would ensure the function f belongs to particular subclasses of S. For an analytic function f(z) = z+ P1n =2 anzn 2 A satisfying the inequality P1n =2 n(n1)janj , a sharp bound on is determined so that f is either starlike or convex of order . A sharp bound on is obtained that ensures functions f satisfying P1n =2 n2+(1 )n janj 1 is either starlike or convex of order . | en_US |
| dc.identifier.uri | http://hdl.handle.net/123456789/7266 | |
| dc.language.iso | en | en_US |
| dc.publisher | Universiti Sains Malaysia | en_US |
| dc.subject | Inclusion Properties Of Linear Operators | en_US |
| dc.subject | Analytic Functions | en_US |
| dc.title | Inclusion Properties Of Linear Operators And Analytic Functions | en_US |
| dc.type | Thesis | en_US |
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