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Title

New inequalities of CBS-type for power series of complex numbers

Authors

Year of publication

2016

Published in

Fasciculi Mathematici

Journal year: 2016 | Journal number: nr 57

Article type

scientific article

Publication language

english

Keywords
EN
  • power series
  • CBS-type inequalities
Abstract

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.

Pages (from - to)

37 - 51

DOI

10.1515/fascmath-2016-0015

License type

CC BY-NC-ND (attribution - noncommercial - no derivatives)

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Access level to full text

public

Points of MNiSW / journal

10.0

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