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September 10, 2025FilomatOpen Access

On contractions involving an auxiliary mapping and fixed-point results

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This work reveals the existence and uniqueness of fixed points in metric spaces, suggesting new iterative algorithms.

The study presents two classes of mappings that fulfill contraction conditions using auxiliary mappings.
Existence and uniqueness of fixed points for these mappings are thoroughly analyzed and demonstrated.
Iterative algorithms designed to converge to fixed points are introduced, with quantifiable convergence errors.
Specific auxiliary mappings allow for the recovery of classical results such as Banach and Kannan fixed-point theorems.

Bessem Samet (2025) studied this question.

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