# On The Development of Nonlinear Operator Theory

## TL;DR

This paper develops foundational results in nonlinear operator theory, extending classical theorems like uniform boundedness and Hahn-Banach to nonlinear contexts, with applications to operators on spaces of bounded linear functionals.

## Contribution

It introduces nonlinear versions of key classical theorems and demonstrates how mappings from metrizable spaces can be embedded into normed spaces.

## Key findings

- Nonlinear uniform boundedness theorem established
- Nonlinear Hahn-Banach theorem formulated
- Mappings from metrizable to normed spaces characterized

## Abstract

The basic results for nonlinear operators are given. These results include nonlinear versions of classical uniform boundedness theorem and Hahn-Banach theorem. Furthermore, the mappings from a metrizable space into another normed space can fall in some normed spaces by defining suitable norms. The results for the mappings on the metrizable spaces can be applied to the operators on the space of bounded linear functionals corresponding to the Dirac's delta function.