# Fixed point-based stability analysis of climate and Langevin models

## TL;DR

This paper explores how fixed point theory can help analyze the stability of climate and Langevin models.

## Contribution

The paper introduces fixed point-based methods to assess stability and consistency in climate and Langevin models.

## Key findings

- Fixed point theory is applied to prove the existence and uniqueness of solutions in climate models.
- Various contraction types are reviewed for their relevance to model stability.
- Theoretical foundations are linked to practical applications in model analysis.

## Abstract

In this manuscript, the existence and uniqueness of solutions to equations associated with climate change are discussed. For this purpose, we utilize some results from the existing literature to investigate the behavior of these equations. Additionally, the role of fixed point theory in emphasizing the importance of proving the stability and consistency of the models is explored. Several definitions and results, such as the F-contraction, α-F-contraction, rational type (ψ,ϕ)-contraction, and Geraghty type contraction, are recalled from the existing literature to illustrate their theoretical foundations and practical applications.