Generalized classes of starlike and convex functions of order α
We have introduced, in this paper, the generalized classes of starlike and convex functions of order α by using the fractional calculus. We then proved some subordination theorems, argument theorems, and various results of modified Hadamard product for functions belonging to these classes. We have a...
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| Format: | Article |
| Language: | English |
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Wiley
1985-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171285000503 |
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| _version_ | 1832552881765482496 |
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| author | Shigeyoshi Owa C. Y. Shen |
| author_facet | Shigeyoshi Owa C. Y. Shen |
| author_sort | Shigeyoshi Owa |
| collection | DOAJ |
| description | We have introduced, in this paper, the generalized classes of starlike and convex functions of order α by using the fractional calculus. We then proved some subordination theorems, argument theorems, and various results of modified Hadamard product for functions belonging to these classes. We have also established some properties about the generalized Libera operator defined on these classes of functions. |
| format | Article |
| id | doaj-art-d3e46958a1e14daebe3778426bb37e7b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1985-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-d3e46958a1e14daebe3778426bb37e7b2025-02-03T05:57:34ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251985-01-018345546710.1155/S0161171285000503Generalized classes of starlike and convex functions of order αShigeyoshi Owa0C. Y. Shen1Department of Mathematics, Kinki University, Higashi-Osaka, Osaka 577, JapanDepartment of Mathematics and Statistics, Simon Fraser University, Burnaby, B.C. V5A 1S6, CanadaWe have introduced, in this paper, the generalized classes of starlike and convex functions of order α by using the fractional calculus. We then proved some subordination theorems, argument theorems, and various results of modified Hadamard product for functions belonging to these classes. We have also established some properties about the generalized Libera operator defined on these classes of functions.http://dx.doi.org/10.1155/S0161171285000503subordinationfractional derivativefractional integralgeneralized Libera operator. |
| spellingShingle | Shigeyoshi Owa C. Y. Shen Generalized classes of starlike and convex functions of order α International Journal of Mathematics and Mathematical Sciences subordination fractional derivative fractional integral generalized Libera operator. |
| title | Generalized classes of starlike and convex functions of order α |
| title_full | Generalized classes of starlike and convex functions of order α |
| title_fullStr | Generalized classes of starlike and convex functions of order α |
| title_full_unstemmed | Generalized classes of starlike and convex functions of order α |
| title_short | Generalized classes of starlike and convex functions of order α |
| title_sort | generalized classes of starlike and convex functions of order α |
| topic | subordination fractional derivative fractional integral generalized Libera operator. |
| url | http://dx.doi.org/10.1155/S0161171285000503 |
| work_keys_str_mv | AT shigeyoshiowa generalizedclassesofstarlikeandconvexfunctionsofordera AT cyshen generalizedclassesofstarlikeandconvexfunctionsofordera |