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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
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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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |