The radius of univalence of Bessel functions I
نویسندگان
چکیده
منابع مشابه
Univalence of Bessel Functions
In particular we shall first determine a radius of univalence for the normalized Bessel functions [7>(z)]1/" for values of v belonging to the region G defined by the inequalities 6{\v} >0, | arg »»| <7r/4. Then we shall determine the radius of univalence of the functions z1_"7,.(z) for values of v belonging to a subset of the closure of G. When v is real and positive we shall determine the exac...
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By using norm estimates of the pre-Schwarzian derivatives for certain family of analytic functions, we shall give simple sufficient conditions for univalence of analytic functions.
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Let A denote the family of all analytic functions f in the unit disk D with the normalization f (0) = 0 = f ′(0)− 1. Define S = { f ∈ A : f is univalent in D}, U = { f ∈A : ∣∣ f ′(z)(z/ f (z))2−1∣∣< 1 for z ∈ D}, and P(1/2) = { f ∈A : Re( f (z)/z) > 1/2 for z ∈ D}. In this paper, we determine the radius of univalency of F(z) = z f (z)/g(z) whenever f ∈S or U , and g ∈S or P(1/2). Based on our i...
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چکیده ندارد.
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cement is an essential ingredient in the concrete buildings. for production of cement considerable amount of fossil fuel and electrical energy is consumed. on the other hand for generating one tone of portland cement, nearly one ton of carbon dioxide is released. it shows that 7 percent of the total released carbon dioxide in the world relates to the cement industry. considering ecological issu...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 1960
ISSN: 0019-2082
DOI: 10.1215/ijm/1255455740