Modified Noor iterations with errors for generalized strongly \(\Phi\)-pseudocontractive maps in Banach spaces. (English) Zbl 1446.47087
Summary: In this paper, we prove some strong convergence results for a family of three generalized strongly \(\Phi\)i-pseudocontractive (accretive) mappings in Banach spaces. Our results are generalizations and improvements of convergence results obtained by several authors in the literature. In particular, they generalize and improve the results of J. O. Olaleru and A. A. Mogbademu [“On the modified Noor iteration scheme for nonlinear maps”, Acta Math. Univ. Comen. (2011), https://www.emis.de/journals/AMUC/_inpress/_mogbademu/mogbademurea.pdf], Z.-Q. Xue and R.-Q. Fan [Appl. Math. Comput. 206, No. 1, 12–15 (2008; Zbl 1155.65346)], which is in turn a correction of A. Rafiq [Appl. Math. Comput. 182, No. 1, 589–595 (2006; Zbl 1120.65074)].
MSC:
| 47J26 | Fixed-point iterations |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 47H06 | Nonlinear accretive operators, dissipative operators, etc. |
Keywords:
Noor iterative scheme with errors; Banach spaces; generalized strongly \(\Phi\)-pseudocontractive operators; unique common fixed point; strongly \(\Phi\)-accretive operators; strong convergenceReferences:
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