Attractive points and convergence theorems of generalized hybrid mapping

Volume 8, Issue 4, pp 354--362 http://dx.doi.org/10.22436/jnsa.008.04.08

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Authors

Yuchun Zheng - School of Mathematics and Information Science, Henan Normal University, XinXiang, 453007, P. R. China.

Abstract

In this paper, by means of the concept of attractive points of a nonlinear mapping, we prove strong convergence theorem of the Ishikawa iteration for an (\(\alpha,\beta\))-generalized hybrid mapping in a uniformly convex Banach space, and obtain weak convergence theorem of the Ishikawa iteration for such a mapping in a Hilbert space.

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Keywords

• Attractive points
• generalized hybrid mapping
• Ishikawa iteration
• Mann iteration
• Xu's inequality.

MSC

•  47H10
•  54H25
•  49J40
•  47H05
•  47H04
•  65J15

References

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