Sami ATAILIA (2021) Points Fixes et Géométrie des Espaces de Banach. University Of Souk Ahras
This thesis is devoted to the fixed point theory and its link with the geometry of Banach
spaces. More precisely, we are interested to the study of the existence of the fixed points
for some classes of self-mappings called "generalized nonexpansive" containing the class of
Suzuki mappings with Hardy-Rogers type and those of (c)-mappings and Khan mappings.
The topological properties of the set of fixed points associated with these classes are
analyzed on various Banach spaces. Furthermore, the convergence of certain iterative
processes to the fixed points is also established.
Keywords: Fixed point, Banach space, generalized nonexpansive mappings, uniformly
convex Banach space, strictly convex Banach space, (c)-mapping, Suzuki mapping of
Hardy-Rogers type, iterative process.