Théorie des points fixes communs pour les f-contractions commutatives : Généralisations et applications

Abstract

This thesis advances fixed-point theory by introducing innovative generalizations, particularly for commutative F-contractions. It establishes more flexible conditions than the classical Banach and Jungck theorems, ensuring the existence and uniqueness of common fixed points. The results rely on topological assumptions, such as the boundedness of iterative sequences, rather than strict algebraic constraints. Applications in numerical analysis and dynamical systems modeling demonstrate the practical relevance of these advancements. The proposed methods, including non-commutative hybrid techniques, expand possibilities for optimization problems. The thesis also explores extensions to generalized metric spaces and asymptotic contractions. Rigorous proofs, supported by examples, validate the proposed approaches. Finally, future research directions are outlined to adapt these results to multidisciplinary contexts. This work thus serves as a benchmark for subsequent studies in functional analysis and applied mathematics.