A Note on "Implicit Mann Fixed Point Iterations for Pseudo-Contractive Mappings"

Abstract:

Ljubomir Ciric, Arif Rafiq, Nenad Cakic, Jeong Sheok Umed [ Implicit Mann fixed point iterations for pseudo-contractive mappings, Applied Mathematics Letters 22 (2009) 581-584] introduced and investigated a modified Mann implicit iteration process for continuous hemi-contractive map. They proved the relatively convergence theorem. However, the content of mann theorem is fuzzy. In this paper, we will give some comments . Let be a Banach space and be a nonempty subset of . A mapping is called hemi-contractive (see [1]) if and In [1], the authors introduced and investigated a modified Mann implicit iteration process for continuous hemi-contractive map. They proved the following convergence theorem.

• Periodical: Advanced Materials Research (Volumes 393-395)
• Pages: 543-545
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.393-395.543
• Online since: November 2011
• Authors: Hong Jun Li, Yong Fu Su
• Keywords: Fixed Point, Hemi-Contractive Mapping, Hilbert Space, Implicit-Mann-Type Iteration Process

References

[1] Ljubomir Ciric, Arif Rafiq, Nenad Cakic, Jeong Sheok Umed, Implicit Mann fixed point iterations for pseudo-contractive mappings, Applied Mathematics Letters 22 (2009) 581-584.

DOI: 10.1016/j.aml.2008.06.034