Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4643151 | Journal of Computational and Applied Mathematics | 2006 | 14 Pages |
Abstract
For β<1 and γ⩾0, let Pγ(β) denote the class of all normalized analytic functions f in the unit disc such thatReeiη(1-γ)f(z)z+γfâ²(z)-β>0,zâÎ,for some ηâR. For fâPγ(β), we consider the integral transformVλ(f)(z)=â«01λ(t)f(tz)tdt,where λ(t) is a real-valued nonnegative weight function so that â«01λ(t)dt=1. The main aim of this paper is to find conditions such that Vλ(f)âP1(α) whenever fâPγ(β) for γ⩾1. We also obtain conditions such that Vλ(f)âP1(βâ²) whenever fâP0(β) for various choices of λ(t). As a useful consequence, we find conditions for certain hypergeometric functions to be univalent.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
R.W. Barnard, S. Naik, S. Ponnusamy,