On approximate roots of polynomials and systems of polynomials in ultrametric Banach algebras

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:464

Article

Brzdek, Janusz¹  Jablonska, Eliza²  Olko, Jolanta³ 

[1] Pedag Univ, Dept Math, Podchorazych 2, PL-30084 Krakow, Poland

[2] Rzeszow Univ Technol, Dept Discrete Math, Powstancow Warszawy 12, PL-35959 Rzeszow, Poland

[3] AGH Univ Sci & Technol, Fac Appl Math, Mickiewicza 30, PL-30059 Krakow, Poland

关键词: System of polynomials;    Approximate root;    Ultrametric Banach algebra;    Nonlinear operator;    Almost everywhere;    Ulam stability;   

DOI  :  10.1016/j.jmaa.2018.04.027

来源: Elsevier

【 摘 要 】

We present methods that allow to estimate the distance between the approximate and exact zeros of some polynomial equations and systems of them (also infinite) in ultrametric Banach algebras. To make our results more useful, we consider that issue in a more general situation, i.e., for some functional equations of polynomial form; moreover, we do it almost everywhere (with respect to a given sigma-ideal). As an auxiliary tool we prove an ultrametric version of a fixed point theorem in some function spaces (also almost everywhere). Our investigations have been motivated by several previous outcomes and the notion of Ulam stability. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free