Volume integral means of holomorphic functions
نویسندگان
چکیده
منابع مشابه
Volume Integral Means of Holomorphic Functions
The classical integral means of a holomorphic function f in the unit disk are defined by [ 1 2π ∫ 2π 0 |f(re)| dθ ]1/p , 0 ≤ r < 1. These integral means play an important role in modern complex analysis. In this note we consider integral means of holomorphic functions in the unit ball Bn in C with respect to weighted volume measures, Mp,α(f, r) = [ 1 vα(rBn) ∫ rBn |f(z)| dvα(z) ]1/p , 0 ≤ r < 1...
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For analytic functions f(z) and g(z) which satisfy the subordination f(z) ≺ g(z), J. E. Littlewood (Proc. London Math. Soc., 23 (1925), 481–519) has shown some interesting results for integral means of f(z) and g(z). The object of the present paper is to derive some applications of integral means by J.E. Littlewood and show interesting examples for our theorems. We also generalize the results o...
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We introduce the analytic functions f (z) = z + ∞ ∑ k=n+1 akz k ( n ∈ N) and p(z) = z + m ∑ s=1 bsj−s+1zsj−s+1 (j ≥ n + 1;n ∈ N) in the open unit disk U. By means of the subordination theorem of J.E. Littlewood, we shall investigate the integral means with coefficients inequalities of analytic functions f(z) and p(z). Some applications of the integral mean of f(z) are considered. 2000 Mathemati...
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For analytic and multivalent functions f (z) and p(z) in the open unit disk U, a subordi-nation theorem due to Littlewood (1925) which was called the integral mean is applied. Some simple examples for our results are also considered.
متن کاملIntegral Means of Analytic Mappings by Iteration of Janowski Functions
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2011
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-2010-10797-9