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 |
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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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| _version_ | 1850224261402198016 |
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| author | Sarika Verma Sushma Gupta Sukhjit Singh |
| author_facet | Sarika Verma Sushma Gupta Sukhjit Singh |
| author_sort | Sarika Verma |
| collection | DOAJ |
| description | 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 . |
| format | Article |
| id | doaj-art-51d3fb5cb31d4cc0b122001cd04140de |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-51d3fb5cb31d4cc0b122001cd04140de2025-08-20T02:05:41ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/259054259054On an Integral Transform of a Class of Analytic FunctionsSarika Verma0Sushma Gupta1Sukhjit Singh2Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal 148106, IndiaDepartment of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal 148106, IndiaDepartment of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal 148106, IndiaFor 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 .http://dx.doi.org/10.1155/2012/259054 |
| spellingShingle | Sarika Verma Sushma Gupta Sukhjit Singh On an Integral Transform of a Class of Analytic Functions Abstract and Applied Analysis |
| title | On an Integral Transform of a Class of Analytic Functions |
| title_full | On an Integral Transform of a Class of Analytic Functions |
| title_fullStr | On an Integral Transform of a Class of Analytic Functions |
| title_full_unstemmed | On an Integral Transform of a Class of Analytic Functions |
| title_short | On an Integral Transform of a Class of Analytic Functions |
| title_sort | on an integral transform of a class of analytic functions |
| url | http://dx.doi.org/10.1155/2012/259054 |
| work_keys_str_mv | AT sarikaverma onanintegraltransformofaclassofanalyticfunctions AT sushmagupta onanintegraltransformofaclassofanalyticfunctions AT sukhjitsingh onanintegraltransformofaclassofanalyticfunctions |