Common Fixed Point Results for Some Class of Generalized Nonexpansive Mappings in Banach Spaces
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Date
2025-06
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Addis Ababa University
Abstract
This study explores generalizations of nonexpansive mappings, focusing on two commuting mappings that satisfy the Bγ,μ condition. We used some algorithm for approximating a common fixed point on some class of generalized nonexpansive mappings and proved its strong convergence to a common _xed point. Our _ndings extend and enhance several recent results
in the literature.
We discussed the properties of generalized nonexpansive mappings, particularly emphasizing
a sequence of commuting mappings that satisfy the B;_ condition. We proposed iterative
algorithms for approximating a common _xed point for these sequences, demonstrating their
convergence under mild assumptions on the parameters.
Additionally, we introduced a pair of some class of generalized nonexpansive mappings and
investigated the convergence and existence of common _xed points within this class. We
applied the three-step iteration process of Abbas-Nazir for a pair mappings satisfying some
class of generalized nonexpansive on a nonempty subset of a Banach space. This approach
yielded results related to both strong and weak convergence, leading to the identi_cation of
the common _xed point of the two mappings. Finally, we provided an example illustrating
two mappings that satisfy the speci_ed conditions.
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Keywords
Common Fixed Point Results, Some Class of Generalized Nonexpansive Mappings, Banach Spaces, Nonexpansive Mappings