A new faster iteration process to fixed points of generalized α-nonexpansive mappings in Banach spaces | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 1، دوره 15، شماره 5، مرداد 2024، صفحه 1-10 اصل مقاله (365.61 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.23025.2460 | ||
| نویسندگان | ||
| Asghar Rahimi1؛ Ali Rezaei2؛ Bayaz Daraby2؛ Mostafa Ghasemi* 2 | ||
| 1Department of Mathematics, University of Maragheh, Maragheh, Iran | ||
| 2Department of Mathematics, University of Maragheh, Maragheh, Iran | ||
| چکیده | ||
| In this paper, we introduce a new iterative scheme to approximate the fixed point of generalized α-nonexpansive mappings. we first prove that the proposed iteration process is faster than all of Picard, Mann, Ishikawa, Noor, Agarwal, Abbas and Thakur processes for contractive mappings. We also obtain some weak and strong convergence theorems for generalized α-nonexpansive mappings. Using the example presented in [R. Pant and R. Shukla, Approximating fixed point of generalized α-nonexpansive mappings in Banach spaces, J. Numer. Funct. Anal. Optim. 38(2017) 248-266.], we compare the convergence behavior of the new iterative process with other iterative processes. | ||
| کلیدواژهها | ||
| Uniformly convex Banach space؛ Convergence theorem؛ Generalized α-nonexpansive mapping؛ Opial property؛ Iterative process | ||
| مراجع | ||
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