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Let 𝓐 denote the class of all analytic functions f in the open unit disc 𝔻 in the complex plane satisfying f(0) = 0, f'(0) = 1. Let U(λ) (0 < λ ≤ 1) denote the class of functions f ∈ 𝓐 for which
|(z/f(z))²f'(z) -1| < λ for z ∈ 𝔻.
The behaviour of functions in this class has been extensively studied in the literature. In this paper, we shall prove that no member of U₀(λ) = {f ∈ U(λ): f''(0) = 0} is convex in 𝔻 for any λ and obtain a lower bound for the...
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