Subordination by convex functions
Let K(α), 0≤α<1, denote the class of functions g(z)=z+Σn=2∞anzn which are regular and univalently convex of order α in the unit disc U. Pursuing the problem initiated by Robinson in the present paper, among other things, we prove that if f is regular in U,f(0)=0, and f(z)+zf′(z)<g(z)+zg′(z) in...
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Wiley
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S016117120000140X |
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| author | Ram Singh Sukhjit Singh |
| author_facet | Ram Singh Sukhjit Singh |
| author_sort | Ram Singh |
| collection | DOAJ |
| description | Let K(α), 0≤α<1, denote the class of functions g(z)=z+Σn=2∞anzn which are regular and univalently convex of order α in the unit disc U. Pursuing the problem initiated by Robinson in the present paper, among other things, we prove that if f is regular in U,f(0)=0, and
f(z)+zf′(z)<g(z)+zg′(z) in U, then (i) f(z)<g(z) at least in |z|<r0,r0=5/3=0.745… if f∈K; and (ii) f(z)<g(z) at least in |z|<r1,r1((51−242)/23)1/2=0.8612… if
g∈K(1/2). |
| format | Article |
| id | doaj-art-46822d0cdcf74557a90b048c10c42bb6 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2000-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-46822d0cdcf74557a90b048c10c42bb62025-02-03T01:11:07ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252000-01-0124856356810.1155/S016117120000140XSubordination by convex functionsRam Singh0Sukhjit Singh1Department of Mathematics, Punjabi University, Patiala 147002, (Punjab), IndiaDepartment of Mathematics, Punjabi University, Patiala 147002, (Punjab), IndiaLet K(α), 0≤α<1, denote the class of functions g(z)=z+Σn=2∞anzn which are regular and univalently convex of order α in the unit disc U. Pursuing the problem initiated by Robinson in the present paper, among other things, we prove that if f is regular in U,f(0)=0, and f(z)+zf′(z)<g(z)+zg′(z) in U, then (i) f(z)<g(z) at least in |z|<r0,r0=5/3=0.745… if f∈K; and (ii) f(z)<g(z) at least in |z|<r1,r1((51−242)/23)1/2=0.8612… if g∈K(1/2).http://dx.doi.org/10.1155/S016117120000140XSubordinationconvex functionconvex function of order 1/2. |
| spellingShingle | Ram Singh Sukhjit Singh Subordination by convex functions International Journal of Mathematics and Mathematical Sciences Subordination convex function convex function of order 1/2. |
| title | Subordination by convex functions |
| title_full | Subordination by convex functions |
| title_fullStr | Subordination by convex functions |
| title_full_unstemmed | Subordination by convex functions |
| title_short | Subordination by convex functions |
| title_sort | subordination by convex functions |
| topic | Subordination convex function convex function of order 1/2. |
| url | http://dx.doi.org/10.1155/S016117120000140X |
| work_keys_str_mv | AT ramsingh subordinationbyconvexfunctions AT sukhjitsingh subordinationbyconvexfunctions |