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- Title
On the iterative scheme generating methods using mean-valued sequences.
- Authors
ATSUMASA KONDO
- Abstract
Using the Mann method and the shrinking projection method, we present generalized forms of iterative scheme generating methods and compared them with prior frameworks. To this end, the properties of mean-valued sequences are leveraged. Subsequently, we establish a convergence theorem similar to that developed by Martinez-Yanes and Xu. This approach highlights the difference between the conventional shrinking projection method and the Martinez-Yanes and Xu variant. The proposed frameworks yield various types of iterative schemes for finding common fixed points, including a three-step iterative scheme. The class of mappings considered incorporate general types, including nonexpansive mappings.
- Subjects
NONEXPANSIVE mappings
- Publication
Carpathian Journal of Mathematics, 2024, Vol 40, Issue 3, p819
- ISSN
1584-2851
- Publication type
Article
- DOI
10.37193/CJM.2024.03.18