Journals / Hacettepe Journal of Mathematics and Statistics / 2011 / Cilt: 40 - Sayı: 3

An iterative algorithm combining the viscosity method with the parallel method for a finite family of uniformly l-Lipschitzian mappings

Pages
453–460
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The results presented in the paper improve and extend some recent results announced by Chang, Ofoedu, Schu and Zeng, and many others.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The purpose of this paper is to prove a strong convergence theorem for a finite family of uniformly L-Lipschitzian mappings through the viscosity parallel iterative algorithm in Banach spaces.
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Key Findings & Data:The purpose of this paper is to prove a strong convergence theorem for a finite family of uniformly L-Lipschitzian mappings through the viscosity parallel iterative algorithm in Banach spaces.
💡
Conclusion & Impact:The results presented in the paper improve and extend some recent results announced by Chang, Ofoedu, Schu and Zeng, and many others.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

The purpose of this paper is to prove a strong convergence theorem for a finite family of uniformly L-Lipschitzian mappings through the viscosity parallel iterative algorithm in Banach spaces. The results presented in the paper improve and extend some recent results announced by Chang, Ofoedu, Schu and Zeng, and many others.

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Cite This Article

GU, F. (2022). An iterative algorithm combining the viscosity method with the parallel method for a finite family of uniformly l-Lipschitzian mappings. Hacettepe Journal of Mathematics and Statistics, Cilt: 40 - Sayı: 3, 453–460. https://ajindex.com/articles/530611

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References (1)

  1. Chang, S. S. Some results for asymptotically pseudo-contractive mappings and asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 129, 845-853, 2001. [2]Chang, S. S. On Chidume's open questions and approximation solutions of multi-valued strongly accretive mapping equation in Banach spaces, J. Math. Anal. Appl. 216, 94-111, 1997. [3]Gobel, K and Kirk, W. A. A fixed points theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 35, 171-174, 1972. [4]Moore, C. and Nnoli, B. V. Iterative solution of nonlinear equations involving set-valued uniformly accretive operators, Computers Math. Applic. 42, 131-140, 2001. [5]Ofoedu, E. U. Strong convergence theorem for uniformly L-Lipschitzian asymptotically pseu-docontractive mapping in a real Banach space, J. Math. Anal. Appl. 321, 722-728, 2006. [6]Schu, J. Iterative construction of fixed point of asymptotically nonexpansive mappings, J. Math. Anal. Appl. 158, 407-413, 1991. [7]Tan, K. K. and Xu, H. K. Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl. 178,301-308, 1993. [8]Zeng, L. C. On the iterative approximation for asymptotically pseudo-contractive mappings in uniformly smooth Banach spaces (in Chinese), Chinese Math. Ann. 26A:2, 283-290, 2005. [9]Zeng, L. C. On the approximation of fixed points for asymptotically nonexpansive mappings in Banach spaces (in Chinese), Acta Math. Sci. 23A:1, 31-37, 2003.