Convergence and Data Dependency of Normal−S Iterative Method for Discontinuous Operators on Banach Space

ABSTRACT

We study convergence, rate of convergence and data dependency of normal−S iterative method for a fixed point of a discontinuous operator T on a Banach space. We also prove some Collage type theorems for T. The main aim here is to show that there is a close relationship between the concepts of data dependency of fixed points and the collage theorems and show that the latter provides better estimate. Numerical examples in support of the results obtained are also given.

KEYWORDS:

• Collage theorem
• data dependency
• inverse problem
• iterative scheme
• strong convergence

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 65J15
• 65J22
• 47N40
• 47H10

Acknowledgements

The authors would like to thank the anonymous reviewers for their comments to improve presentation of the paper. The author A.R. Khan would like to acknowledge