Some sufficient conditions for univalence and starlikeness
Ram Singh, Sunder Singh (1982)
Colloquium Mathematicae
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Ram Singh, Sunder Singh (1982)
Colloquium Mathematicae
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Yusuf Avci (1991)
Annales Polonici Mathematici
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Singh, Sukhjit (1991)
International Journal of Mathematics and Mathematical Sciences
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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...
Shanmugam, T.N. (1989)
International Journal of Mathematics and Mathematical Sciences
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Goodman, A.W. (1979)
International Journal of Mathematics and Mathematical Sciences
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Salmassi, Mohammad (1986)
International Journal of Mathematics and Mathematical Sciences
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Nunokawa, Mamoru, Owa, Shigeyoshi, Saitoh, Hitoshi, Takahashi, Norihiro (2002)
General Mathematics
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Sumit Nagpal, V. Ravichandran (2012)
Annales Polonici Mathematici
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By using the theory of first-order differential subordination for functions with fixed initial coefficient, several well-known results for subclasses of univalent functions are improved by restricting the functions to have fixed second coefficient. The influence of the second coefficient of univalent functions becomes evident in the results obtained.
Frasin, B.A., Darus, M. (2009)
Journal of Inequalities and Applications [electronic only]
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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.
Wirths, K.-J. (2006)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 30C25, 30C45. Let D denote the open unit disc and f:D→[`C] be meromorphic and injective in D. We further assume that f has a simple pole at the point p О (0,1) and is normalized by f(0) = 0 and f′(0) = 1. In particular, we are concerned with f that map D onto a domain whose complement with respect to [`C] is convex. Because of the shape of f(D) these functions will be called concave univalent functions with pole p and the family of...
K. S. Padmanabhan, R. Manjini (1986)
Publications de l'Institut Mathématique
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Shams, Saeid, Kulkarni, S.R., Jahangiri, Jay M. (2003)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Singh, Sukhjit, Gupta, Sushma (2003)
International Journal of Mathematics and Mathematical Sciences
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