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Geometric properties for convolutions of hypergeometric functions and functions with the derivative in a halfplane
Date Issued
01-01-1999
Author(s)
Indian Institute of Technology, Madras
Rønning, F.
Abstract
For β < 1, let R(β) denote the class of normalized functions f which are regular in the unit disk A and satisfy the condition Re[eiα(f′(z) - β)] > 0 for z ∈ Δ. This paper deals with the following problem: for any given a > 0, b > 0, determine conditions on c and β such that the convolution zF(a, b; c; z) * f(z) is starlike if f ∈ R(β). The same question for the function zΦ(a; c; z) * f(z) is also treated. Here F(a, b; c; z) and Φ(a; c; z) are the Gaussian and confluent hypergeometric functions, respectively.
Volume
8