Perturbation of the mapping and solvability theorems in Banach space

TL;DR

This paper examines how perturbations affect the properties and solvability of equations in Banach spaces, focusing on local behaviors and comparisons with smooth mappings.

Contribution

It introduces new insights into the perturbation effects on mappings and solvability in Banach spaces, including local property analysis and mixed problem studies.

Findings

Perturbations can significantly alter the solvability of equations in Banach spaces.

Local properties of mappings are crucial for understanding their global behavior.

The study provides conditions under which solutions exist despite perturbations.

Abstract

Here we consider a perturbation of continuous mappings on Banach spaces and investigate their image under various conditions. Consequently, we study the solvability of some classes of equations and inclusions. For these, we start by the investigating of local properties of the considered mapping and local comparing this mapping with certain smooth mappings. Moreover, we study different mixed problems.