Convolution theorems for starlike and convex functions in the unit disc
M. Anbudurai, R. Parvatham, S. Ponnusamy, V. Singh (2004)
Annales Polonici Mathematici
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Let A denote the space of all analytic functions in the unit disc Δ with the normalization f(0) = f’(0) − 1 = 0. For β < 1, let . For λ > 0, suppose that denotes any one of the following classes of functions: , , . The main purpose of this paper is to find conditions on λ and γ so that each f ∈ is in or , γ ∈ [0,1/2]. Here and respectively denote the class of all starlike functions of order γ and the class of all convex functions of order γ. As a consequence, we obtain...