New inequalities of CBS-type for power series of complex numbers
2016
scientific article
english
- power series
- CBS-type inequalities
EN Let f (λ) = ∑n=0∞ an λn be a function defned by power series with complex coefficients and convergent on the open disk D (0, R) ⊂ C, R > 0. In this paper we show amongst other that, if α, z ∈ C are such that |α|, |α||z|2 < R, then ∣f (α) f (αz2) − f2(αz)∣ ≤ fA(|α|) fA (|α||z|2) −|fA(|α|z)|2. where fa (z) = ∑n=0∞ |an|zn. Applications for some fundamental functions defined by power series are also provided.
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CC BY-NC-ND (attribution - noncommercial - no derivatives)
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