On the uniqueness of fixed points for nonlinear-linear operator sums of Krasnosel’skii type: On the uniqueness of fixed points

Soukaina El Bazi; Ahmed Zeghal

doi:10.5269/bspm.79280

On the uniqueness of fixed points for nonlinear-linear operator sums of Krasnosel’skii type

On the uniqueness of fixed points

Authors

Soukaina El Bazi Abdelmalek Essaâdi University, FST Tangier
Pr. A. Zeghal Abdelmalek Essaadi University, FST of Tangier https://orcid.org/0000-0002-8284-4308

DOI:

https://doi.org/10.5269/bspm.79280

Abstract

This paper extends Kellogg’s uniqueness fixed point theorem within the framework of Krasnosel’skii’s fixed point theorem. More precisely, we provide sufficient conditions on a linear operator B and a nonlinear mapping A to ensure the unique

ness of the fixed point of the mapping A+B. We also investigate the global asymp

totic stability of this fixed point in connection with the Belitskii-Lyubich conjecture.

An illustrative application of the main theoretical result is presented.