On close-to-convex functions of complex order
The class S*(b) of starlike functions of complex order b was introduced and studied by M.K. Aouf and M.A. Nasr. The authors using the Ruscheweyh derivatives introduce the class K(b) of functions close-to-convex of complex order b, b≠0 and its generalization, the classes Kn(b) where n is a nonnegativ...
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| Format: | Article |
| Language: | English |
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Wiley
1990-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171290000473 |
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| author | H. S. Al-Amiri Thotage S. Fernando |
| author_facet | H. S. Al-Amiri Thotage S. Fernando |
| author_sort | H. S. Al-Amiri |
| collection | DOAJ |
| description | The class S*(b) of starlike functions of complex order b was introduced and studied by M.K. Aouf and M.A. Nasr. The authors using the Ruscheweyh derivatives introduce the class K(b) of functions close-to-convex of complex order b, b≠0 and its generalization, the classes Kn(b) where n is a nonnegative integer. Here S*(b)⊂K(b)=K0(b). Sharp coefficient bounds are determined for Kn(b) as well as several sufficient conditions for functions to belong to Kn(b). The authors also obtain some distortion and covering theorems for Kn(b) and determine the radius of the largest disk in which every f∈Kn(b) belongs to Kn(1). All results are sharp. |
| format | Article |
| id | doaj-art-edb3d162f90742bca28970e53c9a36cc |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1990-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-edb3d162f90742bca28970e53c9a36cc2025-02-03T06:13:14ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251990-01-0113232133010.1155/S0161171290000473On close-to-convex functions of complex orderH. S. Al-Amiri0Thotage S. Fernando1Department of Mathematics and Statistics, Bowling Green State University, Bowling Green 43403, OH, USADepartment of Mathematics and Statistics, Bowling Green State University, Bowling Green 43403, OH, USAThe class S*(b) of starlike functions of complex order b was introduced and studied by M.K. Aouf and M.A. Nasr. The authors using the Ruscheweyh derivatives introduce the class K(b) of functions close-to-convex of complex order b, b≠0 and its generalization, the classes Kn(b) where n is a nonnegative integer. Here S*(b)⊂K(b)=K0(b). Sharp coefficient bounds are determined for Kn(b) as well as several sufficient conditions for functions to belong to Kn(b). The authors also obtain some distortion and covering theorems for Kn(b) and determine the radius of the largest disk in which every f∈Kn(b) belongs to Kn(1). All results are sharp.http://dx.doi.org/10.1155/S0161171290000473starlike functionsclose-to-convex functions of complex orderRuscheweyh derivativesHadamard product. |
| spellingShingle | H. S. Al-Amiri Thotage S. Fernando On close-to-convex functions of complex order International Journal of Mathematics and Mathematical Sciences starlike functions close-to-convex functions of complex order Ruscheweyh derivatives Hadamard product. |
| title | On close-to-convex functions of complex order |
| title_full | On close-to-convex functions of complex order |
| title_fullStr | On close-to-convex functions of complex order |
| title_full_unstemmed | On close-to-convex functions of complex order |
| title_short | On close-to-convex functions of complex order |
| title_sort | on close to convex functions of complex order |
| topic | starlike functions close-to-convex functions of complex order Ruscheweyh derivatives Hadamard product. |
| url | http://dx.doi.org/10.1155/S0161171290000473 |
| work_keys_str_mv | AT hsalamiri onclosetoconvexfunctionsofcomplexorder AT thotagesfernando onclosetoconvexfunctionsofcomplexorder |