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The Convergence of Three-Step Iterative Schemes for Generalized Hemi-Contractive Mappings and the Comparison of Their Rate of Convergence
Journal of Mathematics ( IF 1.4 ) Pub Date : 2021-07-22 , DOI: 10.1155/2021/9064369
Linxin Li 1 , Dingping Wu 1
Affiliation  

Charles proved the convergence of Picard-type iteration for generalized accretive nonself-mappings in a real uniformly smooth Banach space. Based on the theorems of the zeros of strongly quasi-accretive mappings and fixed points of strongly hemi-contractions, we extend the results to Noor iterative process and SP iterative process for generalized hemi-contractive mappings. Finally, we analyze the rate of convergence of four iterative schemes, namely, Noor iteration, iteration of Corollary 2, SP iteration, and iteration of Corollary 4.

中文翻译:

广义半收缩映射三步迭代方案的收敛性及其收敛率比较

Charles 证明了 Picard 型迭代在真正均匀平滑的 Banach 空间中用于广义增值非自映射的收敛性。基于强拟增积映射的零点定理和强半收缩映射的不动点定理,我们将结果推广到广义半收缩映射的Noor迭代过程和SP迭代过程。最后,我们分析了四种迭代方案的收敛速度,即Noor迭代、Corollary 2的迭代、SP迭代和Corollary 4的迭代。
更新日期:2021-07-22
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