On an Integral Transform of a Class of Analytic Functions
For and , let denote the class of all normalized analytic functions in the open unit disc such that , for some . It is known (Noshiro (1934) and Warschawski (1935)) that functions in are close-to-convex and hence univalent for . For , we consider the integral transform , where is a nonneg...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/259054 |
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| Summary: | For and , let denote the class of all normalized analytic functions in the open unit disc such that ,
for some . It is known (Noshiro (1934) and Warschawski (1935)) that functions in are close-to-convex and hence univalent for . For , we consider the integral transform , where is a nonnegative real-valued integrable function satisfying the condition . The aim of present paper is, for given , to find sharp values of such that (i) whenever and (ii) whenever . |
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| ISSN: | 1085-3375 1687-0409 |