A local surjection theorem with continuous inverse in Banach spaces

TL;DR

This paper proves a local surjection theorem with a continuous inverse for maps between Banach spaces and applies it to inversion problems involving loss of derivatives.

Contribution

It introduces a new local surjection theorem with a continuous right-inverse and applies it to derivative-loss inversion problems.

Findings

Established a local surjection theorem with continuous inverse.

Applied the theorem to specific inversion problems with derivative loss.

Provided theoretical foundations for inverse problems in Banach spaces.

Abstract

In this paper we prove a local surjection theorem with continuous right-inverse for maps between Banach spaces, and we apply it to a class of inversion problems with loss of derivatives.