Common Fixed Point Results for Some Class of Generalized Nonexpansive Mappings in Banach Spaces
| dc.contributor.advisor | Mengistu Goa (PhD) | |
| dc.contributor.author | Gezahegn Anberber | |
| dc.date.accessioned | 2025-08-17T21:10:42Z | |
| dc.date.available | 2025-08-17T21:10:42Z | |
| dc.date.issued | 2025-06 | |
| dc.description.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. | |
| dc.identifier.uri | https://etd.aau.edu.et/handle/123456789/6831 | |
| dc.language.iso | en_US | |
| dc.publisher | Addis Ababa University | |
| dc.subject | Common Fixed Point Results | |
| dc.subject | Some Class of Generalized Nonexpansive Mappings | |
| dc.subject | Banach Spaces | |
| dc.subject | Nonexpansive Mappings | |
| dc.title | Common Fixed Point Results for Some Class of Generalized Nonexpansive Mappings in Banach Spaces | |
| dc.type | Thesis |