On a class of meromorphic p-valent starlike functions involving certain linear operators
Let ∑p be the class of functions f(z) which are analytic in the punctured disk 𝔼*={z∈ℂ:0<|z|<1}. Applying the linear operator Dn+p defined by using the convolutions, the subclass 𝒯n+p(α) of ∑p is considered. The object of the present paper is to prove that 𝒯n+p(α)⊂𝒯n+p−1(α). Since 𝒯0(α) is the...
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| Format: | Article |
| Language: | English |
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Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S016117120220335X |
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| author | Jin-Lin Liu Shigeyoshi Owa |
| author_facet | Jin-Lin Liu Shigeyoshi Owa |
| author_sort | Jin-Lin Liu |
| collection | DOAJ |
| description | Let ∑p be the class of functions f(z) which are analytic in the punctured disk 𝔼*={z∈ℂ:0<|z|<1}. Applying the linear operator Dn+p defined by
using the convolutions, the subclass 𝒯n+p(α) of ∑p is considered. The object of the present paper is to prove that 𝒯n+p(α)⊂𝒯n+p−1(α). Since 𝒯0(α) is the class of meromorphic p-valent starlike functions of order
α, all functions in 𝒯n+p−1(α) are meromorphic p-valent starlike in the open unit disk
𝔼. Further properties preserving integrals and
convolution conditions are also considered. |
| format | Article |
| id | doaj-art-8bb62f3fc8e1465dad91b4cb0022cc84 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-8bb62f3fc8e1465dad91b4cb0022cc842025-02-03T01:32:52ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-0132527128010.1155/S016117120220335XOn a class of meromorphic p-valent starlike functions involving certain linear operatorsJin-Lin Liu0Shigeyoshi Owa1Department of Mathematics, Yangzhou University, Jiangsu, Yangzhou 225002, ChinaDepartment of Mathematics, Kinki University, Osaka, Higashi-Osaka 577-8502, JapanLet ∑p be the class of functions f(z) which are analytic in the punctured disk 𝔼*={z∈ℂ:0<|z|<1}. Applying the linear operator Dn+p defined by using the convolutions, the subclass 𝒯n+p(α) of ∑p is considered. The object of the present paper is to prove that 𝒯n+p(α)⊂𝒯n+p−1(α). Since 𝒯0(α) is the class of meromorphic p-valent starlike functions of order α, all functions in 𝒯n+p−1(α) are meromorphic p-valent starlike in the open unit disk 𝔼. Further properties preserving integrals and convolution conditions are also considered.http://dx.doi.org/10.1155/S016117120220335X |
| spellingShingle | Jin-Lin Liu Shigeyoshi Owa On a class of meromorphic p-valent starlike functions involving certain linear operators International Journal of Mathematics and Mathematical Sciences |
| title | On a class of meromorphic p-valent starlike functions involving certain linear operators |
| title_full | On a class of meromorphic p-valent starlike functions involving certain linear operators |
| title_fullStr | On a class of meromorphic p-valent starlike functions involving certain linear operators |
| title_full_unstemmed | On a class of meromorphic p-valent starlike functions involving certain linear operators |
| title_short | On a class of meromorphic p-valent starlike functions involving certain linear operators |
| title_sort | on a class of meromorphic p valent starlike functions involving certain linear operators |
| url | http://dx.doi.org/10.1155/S016117120220335X |
| work_keys_str_mv | AT jinlinliu onaclassofmeromorphicpvalentstarlikefunctionsinvolvingcertainlinearoperators AT shigeyoshiowa onaclassofmeromorphicpvalentstarlikefunctionsinvolvingcertainlinearoperators |