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

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

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

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

Resumo

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.