Generalized Alpha-Close-to-Convex Functions
We define the classes Gβ(α,k,γ) as follows: f∈Gβ(α,k,γ) if and only if, for z∈E={z∈ℂ:|z|<1}, |arg{(1-α2z2)f′(z)/e−iβϕ′(z)}|≤γπ/2, 0<γ≤1; α∈[0,1]; β∈(−π/2,π/2), where ϕ is a function of bounded boundary rotation. Coefficient estimates, an inclusion result, arclength problem, and some other pr...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2009/830592 |
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| author | K. Inayat Noor Halit Orhan Saima Mustafa |
| author_facet | K. Inayat Noor Halit Orhan Saima Mustafa |
| author_sort | K. Inayat Noor |
| collection | DOAJ |
| description | We define the classes Gβ(α,k,γ) as follows: f∈Gβ(α,k,γ)
if and only if, for z∈E={z∈ℂ:|z|<1}, |arg{(1-α2z2)f′(z)/e−iβϕ′(z)}|≤γπ/2, 0<γ≤1; α∈[0,1]; β∈(−π/2,π/2),
where ϕ
is a function of bounded boundary rotation. Coefficient estimates, an inclusion
result, arclength problem, and some other properties of these classes are studied. |
| format | Article |
| id | doaj-art-f6f2ab4404d741d4a82cc68bcb21e3c8 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-f6f2ab4404d741d4a82cc68bcb21e3c82025-08-20T02:22:49ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252009-01-01200910.1155/2009/830592830592Generalized Alpha-Close-to-Convex FunctionsK. Inayat Noor0Halit Orhan1Saima Mustafa2Department of Mathematics, COMSATS Institute of Information Technology, Islamabad 44000, PakistanDepartment of Mathematics, Faculty of Science, Ataturk University, 25240 Erzurum, TurkeyDepartment of Mathematics, COMSATS Institute of Information Technology, Islamabad 44000, PakistanWe define the classes Gβ(α,k,γ) as follows: f∈Gβ(α,k,γ) if and only if, for z∈E={z∈ℂ:|z|<1}, |arg{(1-α2z2)f′(z)/e−iβϕ′(z)}|≤γπ/2, 0<γ≤1; α∈[0,1]; β∈(−π/2,π/2), where ϕ is a function of bounded boundary rotation. Coefficient estimates, an inclusion result, arclength problem, and some other properties of these classes are studied.http://dx.doi.org/10.1155/2009/830592 |
| spellingShingle | K. Inayat Noor Halit Orhan Saima Mustafa Generalized Alpha-Close-to-Convex Functions International Journal of Mathematics and Mathematical Sciences |
| title | Generalized Alpha-Close-to-Convex Functions |
| title_full | Generalized Alpha-Close-to-Convex Functions |
| title_fullStr | Generalized Alpha-Close-to-Convex Functions |
| title_full_unstemmed | Generalized Alpha-Close-to-Convex Functions |
| title_short | Generalized Alpha-Close-to-Convex Functions |
| title_sort | generalized alpha close to convex functions |
| url | http://dx.doi.org/10.1155/2009/830592 |
| work_keys_str_mv | AT kinayatnoor generalizedalphaclosetoconvexfunctions AT halitorhan generalizedalphaclosetoconvexfunctions AT saimamustafa generalizedalphaclosetoconvexfunctions |