On certain analytic functions with bounded radius rotation

Certain classes R k ( μ , α ) ; k ≥ 2 , μ > − 1 , 0 ≤ α < 1 of analytic functions are defined in the unit disc using convolution technique. It is shown that functions in R k ( μ , α ) are of bounded radius rotation. It is proved that R k ( μ , α ) and some other newly introduced related classe...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2011-05, Vol.61 (10), p.2987-2993
Main Authors: Noor, Khalida Inayat, Noor, Muhammad Aslam, Al-Said, Eisa A.
Format: Article
Language:English
Subjects:
Analytic functions
Bounded radius rotation
Convolution
Discs
Disks
Functions with positive real part
Integrals
Invariants
Linear operator
Mathematical analysis
Mathematical models
Operators
Ruscheweyh derivative
Starlike
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Summary:Certain classes R k ( μ , α ) ; k ≥ 2 , μ > − 1 , 0 ≤ α < 1 of analytic functions are defined in the unit disc using convolution technique. It is shown that functions in R k ( μ , α ) are of bounded radius rotation. It is proved that R k ( μ , α ) and some other newly introduced related classes are invariant under the generalized Bernardi integral operator. The converse case as a radius problem is also considered. Theorems proved in this paper are best possible in some sense.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2011.03.084