Original scientific paper

Successive approximations for quasi-firmly type nonexpansive mappings

Yisheng Song ; College of Mathematics and Information Science Henan Normal University, XinXiang, HeNan, P.R. China
Qingchun Li ; College of Mathematics and Information Science Henan Normal University, XinXiang, HeNan, P.R. China

Abstract

In this paper, two examples of quasi-firmly type
nonexpansive mappings are given to prove that the concept is different from nonexpansive mapping. Furthermore, it is studied to the convergence of the sequence of successive approximations for this class of mappings only when the super limit of iteration coefficients is less than $1$. In particular, the Picard iteration $\{T^nx_0\}$ of such a mapping converges to a fixed point of $T$ in a compact metric space.

Keywords

quasi-firmly type nonexpansive mappings; Ishikawa-type iteration; Krasnosel\-skii-Mann iteration

Hrčak ID:

68641

URI

https://hrcak.srce.hr/68641

Publication date:

10.6.2011.

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