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On the Rate of Convergence of P-Iteration, SP-Iteration, and D-Iteration Methods for Continuous Nondecreasing Functions on Closed Intervals

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  • Jukkrit Daengsaen
  • Anchalee Khemphet

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.

Suggested Citation

  • Jukkrit Daengsaen & Anchalee Khemphet, 2018. "On the Rate of Convergence of P-Iteration, SP-Iteration, and D-Iteration Methods for Continuous Nondecreasing Functions on Closed Intervals," Abstract and Applied Analysis, Hindawi, vol. 2018, pages 1-6, July.
  • Handle: RePEc:hin:jnlaaa:7345401
    DOI: 10.1155/2018/7345401
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