Meromorphic univalent function with negative coefficient
Let Mn be the classes of regular functions f(z)=z−1+a0+a1z+… defined in the annulus 0<|z|<1 and satisfying ReIn+1f(z)In+1f(z)>0, (n∈ℕ0), where I0f(z)=f(z), If(z)=(z−1−z(z−1)−2)∗f(z), Inf(z)=I(In−1f(z)), and ∗ is the Hadamard convolution. We denote by Γn=Mn⋃Γ, where Γ denotes the class of fu...
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| Format: | Article |
| Language: | English |
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Wiley
1994-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171294000293 |
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| author | A. Dernek |
| author_facet | A. Dernek |
| author_sort | A. Dernek |
| collection | DOAJ |
| description | Let Mn be the classes of regular functions f(z)=z−1+a0+a1z+… defined in the annulus 0<|z|<1 and satisfying ReIn+1f(z)In+1f(z)>0, (n∈ℕ0), where I0f(z)=f(z), If(z)=(z−1−z(z−1)−2)∗f(z), Inf(z)=I(In−1f(z)), and ∗ is the Hadamard convolution. We denote by Γn=Mn⋃Γ, where Γ denotes the class of functions of the form f(z)=z−1+∑k=1∞|ak|zk. We obtained that relates the modulus of the coefficients to starlikeness for the classes Mn and Γn, and coefficient inequalities for the classes Γn. |
| format | Article |
| id | doaj-art-036f001d682a45798dbfd0ca2ff91e3b |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1994-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-036f001d682a45798dbfd0ca2ff91e3b2025-08-20T02:03:17ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251994-01-0117120120310.1155/S0161171294000293Meromorphic univalent function with negative coefficientA. Dernek0Department of Mathematics, Marmara University, Göztepe Kampüsü, Istanbul 81080, TurkeyLet Mn be the classes of regular functions f(z)=z−1+a0+a1z+… defined in the annulus 0<|z|<1 and satisfying ReIn+1f(z)In+1f(z)>0, (n∈ℕ0), where I0f(z)=f(z), If(z)=(z−1−z(z−1)−2)∗f(z), Inf(z)=I(In−1f(z)), and ∗ is the Hadamard convolution. We denote by Γn=Mn⋃Γ, where Γ denotes the class of functions of the form f(z)=z−1+∑k=1∞|ak|zk. We obtained that relates the modulus of the coefficients to starlikeness for the classes Mn and Γn, and coefficient inequalities for the classes Γn.http://dx.doi.org/10.1155/S0161171294000293univalent meromorphic functionsHadamard product. |
| spellingShingle | A. Dernek Meromorphic univalent function with negative coefficient International Journal of Mathematics and Mathematical Sciences univalent meromorphic functions Hadamard product. |
| title | Meromorphic univalent function with negative coefficient |
| title_full | Meromorphic univalent function with negative coefficient |
| title_fullStr | Meromorphic univalent function with negative coefficient |
| title_full_unstemmed | Meromorphic univalent function with negative coefficient |
| title_short | Meromorphic univalent function with negative coefficient |
| title_sort | meromorphic univalent function with negative coefficient |
| topic | univalent meromorphic functions Hadamard product. |
| url | http://dx.doi.org/10.1155/S0161171294000293 |
| work_keys_str_mv | AT adernek meromorphicunivalentfunctionwithnegativecoefficient |