The equivalence between the convergence of the modified Mann and Ishikawa iterations for asymptotically pseudocontractive mappings obtained by dropping the bounded assumption

Journal of inequalities and applications

Guiwen Lv¹ 

关键词: fixed point;    asymptotically pseudocontractive mappings;    modified Mann iteration with errors;    Banach spaces;   

DOI  :  10.1186/1029-242X-2014-293

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we show the equivalence of convergence between the modified Mann and Ishikawa iterations with errors for an asymptotically pseudocontractive mapping under the condition of removing the bounded assumption. We also point out the problems of (Rhoades and Soltuz in J. Math. Anal. Appl. 283:681-688, 2003; Xue in Bull. Korean Math. Soc. 47(2):295-305, 2010; Xue in J. Math. Inequal. 4(3):345-354, 2010), extend and improve the results of (Zeng in Acta Math. Sin. 47(2):219-228, 2004). MSC:47H10, 47H09, 46B20.

【 授权许可】

CC BY