On alpha-close-to-convex functions of order beta
Let Mβ(α)[α≥0 and β≥0] denote the class of all functionsf(z)=z+∑n=2∞anznanalytic in the unit disc U with f′(z)f(z)/z≠0 and which satisfy for z=reiθ∈U the condition ∫θ1θ2Re{(1−α)zf′(z)f(z)+α(1+zf″(z)f′(z))}dθ>−βπ for all θ2>θ1. In this note we show that each f∈Mβ(α) is close-to-star of orde...
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| Format: | Article |
| Language: | English |
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Wiley
1986-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S016117128600056X |
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| _version_ | 1832557137519181824 |
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| author | M. A. Nasr |
| author_facet | M. A. Nasr |
| author_sort | M. A. Nasr |
| collection | DOAJ |
| description | Let Mβ(α)[α≥0 and β≥0] denote the class of all functionsf(z)=z+∑n=2∞anznanalytic in the unit disc U with f′(z)f(z)/z≠0 and which satisfy for z=reiθ∈U the condition ∫θ1θ2Re{(1−α)zf′(z)f(z)+α(1+zf″(z)f′(z))}dθ>−βπ for all θ2>θ1. In this note we show that each f∈Mβ(α) is close-to-star of order β when 0<β≤α. |
| format | Article |
| id | doaj-art-f3e12dab216b422592d672968f62fd04 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1986-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-f3e12dab216b422592d672968f62fd042025-02-03T05:43:33ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251986-01-019343543810.1155/S016117128600056XOn alpha-close-to-convex functions of order betaM. A. Nasr0Faculty of Science, University of Mansoura, Mansoura, EgyptLet Mβ(α)[α≥0 and β≥0] denote the class of all functionsf(z)=z+∑n=2∞anznanalytic in the unit disc U with f′(z)f(z)/z≠0 and which satisfy for z=reiθ∈U the condition ∫θ1θ2Re{(1−α)zf′(z)f(z)+α(1+zf″(z)f′(z))}dθ>−βπ for all θ2>θ1. In this note we show that each f∈Mβ(α) is close-to-star of order β when 0<β≤α.http://dx.doi.org/10.1155/S016117128600056Xclose-to-star functionsclose-to-convex functionsα-convex functions. |
| spellingShingle | M. A. Nasr On alpha-close-to-convex functions of order beta International Journal of Mathematics and Mathematical Sciences close-to-star functions close-to-convex functions α-convex functions. |
| title | On alpha-close-to-convex functions of order beta |
| title_full | On alpha-close-to-convex functions of order beta |
| title_fullStr | On alpha-close-to-convex functions of order beta |
| title_full_unstemmed | On alpha-close-to-convex functions of order beta |
| title_short | On alpha-close-to-convex functions of order beta |
| title_sort | on alpha close to convex functions of order beta |
| topic | close-to-star functions close-to-convex functions α-convex functions. |
| url | http://dx.doi.org/10.1155/S016117128600056X |
| work_keys_str_mv | AT manasr onalphaclosetoconvexfunctionsoforderbeta |