Some classes of alpha-quasi-convex functions
Let C[C,D], −1≤D<C≤1 denote the class of functions g, g(0)=0, g′(0)=1, analytic in the unit disk E such that (zg′(z))′g′(z) is subordinate to 1+CZ1+DZ, z∈E. We investigate some classes of Alpha-Quasi-Convex Functions f, with f(0)=f′(0)−1=0 for which there exists a g∈C[C,D] such that (1−α)f′(z)g′(...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
1988-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171288000584 |
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doaj-67d5e953edf94e3a89e3ea599e1bb0522020-11-25T00:36:43ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251988-01-0111349750110.1155/S0161171288000584Some classes of alpha-quasi-convex functionsKhalida Inayat Noor0Mathematics Department, College of Science Education for Girls, Sitteen Road, Malaz, Riyadh, Saudi ArabiaLet C[C,D], −1≤D<C≤1 denote the class of functions g, g(0)=0, g′(0)=1, analytic in the unit disk E such that (zg′(z))′g′(z) is subordinate to 1+CZ1+DZ, z∈E. We investigate some classes of Alpha-Quasi-Convex Functions f, with f(0)=f′(0)−1=0 for which there exists a g∈C[C,D] such that (1−α)f′(z)g′(z)+α(zf′(z))′g′(z) is subordinate to 1+AZ1+BZ′, −1≤B<A≤1. Integral representation, coefficient bounds are obtained. It is shown that some of these classes are preserved under certain integral operators.http://dx.doi.org/10.1155/S0161171288000584 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Khalida Inayat Noor |
| spellingShingle |
Khalida Inayat Noor Some classes of alpha-quasi-convex functions International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Khalida Inayat Noor |
| author_sort |
Khalida Inayat Noor |
| title |
Some classes of alpha-quasi-convex functions |
| title_short |
Some classes of alpha-quasi-convex functions |
| title_full |
Some classes of alpha-quasi-convex functions |
| title_fullStr |
Some classes of alpha-quasi-convex functions |
| title_full_unstemmed |
Some classes of alpha-quasi-convex functions |
| title_sort |
some classes of alpha-quasi-convex functions |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
1988-01-01 |
| description |
Let C[C,D], −1≤D<C≤1 denote the class of functions g, g(0)=0, g′(0)=1, analytic in the unit disk E such that (zg′(z))′g′(z) is subordinate to 1+CZ1+DZ, z∈E. We investigate some classes of Alpha-Quasi-Convex Functions f, with f(0)=f′(0)−1=0 for which there exists a g∈C[C,D] such that (1−α)f′(z)g′(z)+α(zf′(z))′g′(z) is subordinate to 1+AZ1+BZ′, −1≤B<A≤1. Integral representation, coefficient bounds are obtained. It is shown that some of these classes are preserved under certain integral operators. |
| url |
http://dx.doi.org/10.1155/S0161171288000584 |
| work_keys_str_mv |
AT khalidainayatnoor someclassesofalphaquasiconvexfunctions |
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