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