On the Rate of Convergence of P-Iteration, SP-Iteration, and D-Iteration Methods for Continuous Nondecreasing Functions on Closed Intervals. (2nd July 2018)

• Record Type: Journal Article
• Authors: Daengsaen, Jukkrit; Khemphet, Anchalee
• Other Names: Reich Simeon Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2018(2018)
• Publication Date: 2018-07-02
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2018/7345401
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We introduce a new iterative method called D-iteration to approximate a fixed point of continuous nondecreasing functions on arbitrary closed intervals. The purpose is to improve the rate of convergence compared to previous work. Specifically, our main result shows that D-iteration converges faster than P-iteration and SP-iteration to the fixed point. Consequently, we have that D-iteration converges faster than the others under the same computational cost. Moreover, the analogue of their convergence theorem holds for D-iteration.