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.
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.