Displaying similar documents to “On the Hadamard products of schlicht functions and applications.”

Criteria for univalence, starlikeness and convexity

S. Ponnusamy, P. Vasundhra (2005)

Annales Polonici Mathematici

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Let 𝓐 denote the class of all normalized analytic functions f (f(0) = 0 = f'(0)-1) in the open unit disc Δ. For 0 < λ ≤ 1, define 𝓤(λ) = {f ∈ 𝓐 : |(z/f(z))²f'(z) - 1| < λ, z ∈ Δ} and 𝓟(2λ) = f ∈ 𝓐 : |(z/f(z))''| < 2λ, z ∈ Δ.cr Recently, the problem of finding the starlikeness of these classes has been considered by Obradović and Ponnusamy, and later by Obradović et al. In this paper, the authors consider the problem of finding...

Alternative Characterization of the Class k-UCV and Related Classes of Univalent Functions

Kanas, Stanislawa (1999)

Serdica Mathematical Journal

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In this paper an alternative characterization of the class of functions called k -uniformly convex is found. Various relations concerning connections with other classes of univalent functions are given. Moreover a new class of univalent functions, analogous to the ’Mocanu class’ of functions, is introduced. Some results concerning this class are derived.