Error Estimate of Data Dependence for Discontinuous Operators by New Iteration Process with Convergence Analysis

Abstract

In this paper, we introduce a new discontinuous operator and investigate the existence and uniqueness of fixed points for the operators in complete metric spaces. We also provide rate of convergence and data dependency of S-iterative scheme for a fixed point of the discontinuous operators in Banach spaces. Moreover, we prove the estimation Collage theorems and compare error estimate between data dependency and Collage theorems. Numerical examples are provided to support our results.

Keywords:

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

Mathematics Subject Classification:

• 65J15
• 65J22
• 47H10
• 47N40

Acknowledgments

The second author would like to thank the Research Professional Development Project Under the Science Achievement Scholarship of Thailand (SAST) for financial support.

Disclosure statement

No potential conflict of interest was reported by the authors.

Authors’ contributions

All authors read and approved the final manuscript.

Additional information

Funding

The first author, Wiyada Kumam was financially supported by the Rajamangala University of Technology Thanyaburi (RMUTTT) (Grant No.NSF62D0604). Furthermore, Poom Kumam was supported by the Thailand Research Fund (TRF) and the King Mongkut’s University of Technology Thonburi (KMUTT) under the TRF Research Scholar Award (Grant No.RSA6080047).