Starlikeness associated with certain strongly functions
Let κ be an analytic function in the open unit disc U in the complex plane with κ(0)=1. Then κ∈K(λ) if and only if κ(t)≺ϕλ(t), where ≺ is a subordination relation and the function ϕλ(t):=(1+t)λ, for 0<λ<1, maps U to a symmetric domain about the real axis in the right-half plane. This article f...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-01-01
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| Series: | Heliyon |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844025000830 |
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| author | Afis Saliu Kanwal Jabeen Jianhua Gong Sarfraz Nawaz Malik Hala Alaqad |
| author_facet | Afis Saliu Kanwal Jabeen Jianhua Gong Sarfraz Nawaz Malik Hala Alaqad |
| author_sort | Afis Saliu |
| collection | DOAJ |
| description | Let κ be an analytic function in the open unit disc U in the complex plane with κ(0)=1. Then κ∈K(λ) if and only if κ(t)≺ϕλ(t), where ≺ is a subordination relation and the function ϕλ(t):=(1+t)λ, for 0<λ<1, maps U to a symmetric domain about the real axis in the right-half plane. This article finds the sharp radii of starlikeness for three classes of normalized analytic functions in the open unit disc. It also finds the solutions to first-order differential equations and utilizes these results together with the differential subordination developed by Miller and Mocanu to obtain the conditions so that some first-order differential relations associated with ϕλ are subordinate to certain Ma and Minda functions. Consequently, it provides sufficient conditions for the normalized analytic functions to belong to some established subclasses of starlike functions. |
| format | Article |
| id | doaj-art-428236311fb74f22a7af10b273387f95 |
| institution | Kabale University |
| issn | 2405-8440 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Heliyon |
| spelling | doaj-art-428236311fb74f22a7af10b273387f952025-02-02T05:27:59ZengElsevierHeliyon2405-84402025-01-01112e41703Starlikeness associated with certain strongly functionsAfis Saliu0Kanwal Jabeen1Jianhua Gong2Sarfraz Nawaz Malik3Hala Alaqad4Department of Mathematics, University of The Gambia, P.O. Box 3530, Kanifing, Serrekunda, the GambiaDepartment of Mathematics, COMSATS University Islamabad, Islamabad Campus, Islamabad 45550, PakistanDepartment of Mathematical Sciences, United Arab Emirates University, Al Ain 15551, United Arab Emirates; Corresponding author.Department of Mathematics, COMSATS University Islamabad, Wah Campus, Wah Cantt 47040, PakistanDepartment of Mathematical Sciences, United Arab Emirates University, Al Ain 15551, United Arab EmiratesLet κ be an analytic function in the open unit disc U in the complex plane with κ(0)=1. Then κ∈K(λ) if and only if κ(t)≺ϕλ(t), where ≺ is a subordination relation and the function ϕλ(t):=(1+t)λ, for 0<λ<1, maps U to a symmetric domain about the real axis in the right-half plane. This article finds the sharp radii of starlikeness for three classes of normalized analytic functions in the open unit disc. It also finds the solutions to first-order differential equations and utilizes these results together with the differential subordination developed by Miller and Mocanu to obtain the conditions so that some first-order differential relations associated with ϕλ are subordinate to certain Ma and Minda functions. Consequently, it provides sufficient conditions for the normalized analytic functions to belong to some established subclasses of starlike functions.http://www.sciencedirect.com/science/article/pii/S2405844025000830Strongly functionSubordinationAnalytic functionDifferential subordinationRadius problem |
| spellingShingle | Afis Saliu Kanwal Jabeen Jianhua Gong Sarfraz Nawaz Malik Hala Alaqad Starlikeness associated with certain strongly functions Heliyon Strongly function Subordination Analytic function Differential subordination Radius problem |
| title | Starlikeness associated with certain strongly functions |
| title_full | Starlikeness associated with certain strongly functions |
| title_fullStr | Starlikeness associated with certain strongly functions |
| title_full_unstemmed | Starlikeness associated with certain strongly functions |
| title_short | Starlikeness associated with certain strongly functions |
| title_sort | starlikeness associated with certain strongly functions |
| topic | Strongly function Subordination Analytic function Differential subordination Radius problem |
| url | http://www.sciencedirect.com/science/article/pii/S2405844025000830 |
| work_keys_str_mv | AT afissaliu starlikenessassociatedwithcertainstronglyfunctions AT kanwaljabeen starlikenessassociatedwithcertainstronglyfunctions AT jianhuagong starlikenessassociatedwithcertainstronglyfunctions AT sarfraznawazmalik starlikenessassociatedwithcertainstronglyfunctions AT halaalaqad starlikenessassociatedwithcertainstronglyfunctions |