Continuity of solutions to operator equations with respect to a parameter

A. G. Ramm

Continuity of solutions to operator equations with respect to a parameter

Functional Analysis 2016-09-07 v3

Authors: A. G. Ramm

Abstract

Let $A(k)u(k)=f(k) (1)$ be an operator equation, $X$ and $Y$ are Banach spaces, $k\in\Delta\subset\C$ is a parameter, $A(k):X\to Y$ is a map, possibly nonlinear. Sufficient conditions are given for continuity of $u(k)$ with respect to $k$ . Necessary and sufficient conditions are given for the continuity of $u(k)$ with respect to $k$ in the case of linear operators $A(k)$ .

Keywords

operator theory on banach spaces banach space fixed point in banach spaces

Cite

@article{arxiv.math/0408194,
  title  = {Continuity of solutions to operator equations with respect to a parameter},
  author = {A. G. Ramm},
  journal= {arXiv preprint arXiv:math/0408194},
  year   = {2016}
}

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