On the Largest Disc Mapped by Sum of Convex and Starlike Functions
For a normalized analytic function f defined on the unit disc 𝔻, let ϕ(f,f′,f′′;z) be a function of positive real part in 𝔻, ψ(f,f′,f′′;z) need not have that property in 𝔻, and χ=ϕ+ψ. For certain choices of ϕ and ψ, a sharp radius constant ρ is determined, 0<ρ<1, so that χ(ρz)/ρ maps 𝔻 onto a...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/682413 |
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| author | Rosihan M. Ali Naveen Kumar Jain V. Ravichandran |
| author_facet | Rosihan M. Ali Naveen Kumar Jain V. Ravichandran |
| author_sort | Rosihan M. Ali |
| collection | DOAJ |
| description | For a normalized analytic function f defined on the unit disc 𝔻, let ϕ(f,f′,f′′;z) be a function of positive real part in 𝔻, ψ(f,f′,f′′;z) need not have that property in 𝔻, and χ=ϕ+ψ. For certain choices of ϕ and ψ, a sharp radius constant ρ is determined, 0<ρ<1, so that χ(ρz)/ρ maps 𝔻 onto a specified region in the right half-plane. |
| format | Article |
| id | doaj-art-59c78d4c92a24a249f9fd344ce46c07a |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-59c78d4c92a24a249f9fd344ce46c07a2025-02-03T06:08:01ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/682413682413On the Largest Disc Mapped by Sum of Convex and Starlike FunctionsRosihan M. Ali0Naveen Kumar Jain1V. Ravichandran2School of Mathematical Sciences, Universiti Sains Malaysia (USM), 11800 Penang, MalaysiaDepartment of Mathematics, University of Delhi, Delhi 110007, IndiaDepartment of Mathematics, University of Delhi, Delhi 110007, IndiaFor a normalized analytic function f defined on the unit disc 𝔻, let ϕ(f,f′,f′′;z) be a function of positive real part in 𝔻, ψ(f,f′,f′′;z) need not have that property in 𝔻, and χ=ϕ+ψ. For certain choices of ϕ and ψ, a sharp radius constant ρ is determined, 0<ρ<1, so that χ(ρz)/ρ maps 𝔻 onto a specified region in the right half-plane.http://dx.doi.org/10.1155/2013/682413 |
| spellingShingle | Rosihan M. Ali Naveen Kumar Jain V. Ravichandran On the Largest Disc Mapped by Sum of Convex and Starlike Functions Abstract and Applied Analysis |
| title | On the Largest Disc Mapped by Sum of Convex and Starlike Functions |
| title_full | On the Largest Disc Mapped by Sum of Convex and Starlike Functions |
| title_fullStr | On the Largest Disc Mapped by Sum of Convex and Starlike Functions |
| title_full_unstemmed | On the Largest Disc Mapped by Sum of Convex and Starlike Functions |
| title_short | On the Largest Disc Mapped by Sum of Convex and Starlike Functions |
| title_sort | on the largest disc mapped by sum of convex and starlike functions |
| url | http://dx.doi.org/10.1155/2013/682413 |
| work_keys_str_mv | AT rosihanmali onthelargestdiscmappedbysumofconvexandstarlikefunctions AT naveenkumarjain onthelargestdiscmappedbysumofconvexandstarlikefunctions AT vravichandran onthelargestdiscmappedbysumofconvexandstarlikefunctions |