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

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 σ-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.