대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제26권2호
  • /
  • Pages.229-235
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  • 2011
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  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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CONVERGENCE OF ISHIKAWA ITERATION WITH ERROR TERMS ON AN ARBITRARY INTERVAL

  • Yuan, Qing (College of Science Hangzhou Normal University) ;
  • Cho, Sun-Young (Department of Mathematics Gyeongsang National University) ;
  • Qin, Xiaolong (College of Science Hangzhou Normal University)
  • 투고 : 2009.07.22
  • 발행 : 2011.04.30
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초록

In this paper, a continuous real function on the real line is considered. The necessary and sufficient conditions for the convergence of the Ishikawa iteration with error terms for the functional are obtained.

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참고문헌

  1. D. Borwein and J. Borwein, Fixed point iterations for real functions, J. Math. Anal. Appl. 157 (1991), no. 1, 112-126. https://doi.org/10.1016/0022-247X(91)90139-Q
  2. R. L. Franks and R. P. Marzec, A theorem on mean value iterations, Proc. Amer. Math. Soc. 30 (1971), 324-326. https://doi.org/10.1090/S0002-9939-1971-0280656-9
  3. S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc. 44 (1974), 147-150. https://doi.org/10.1090/S0002-9939-1974-0336469-5
  4. W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506-510. https://doi.org/10.1090/S0002-9939-1953-0054846-3
  5. Y. Qing and L. Qihou, The necessary and sufficient condition for the convergence of Ishikawa iteration on an arbitrary interval, J. Math. Anal. Appl. 323 (2006), no. 2, 1383-1386. https://doi.org/10.1016/j.jmaa.2005.11.058
  6. B. E. Rhoades, Fixed point iterations using infinite matrices, Trans. Amer. Math. Soc. 196 (1974), 161-176. https://doi.org/10.1090/S0002-9947-1974-0348565-1

피인용 문헌

  1. Convergence theorems for continuous functions on an arbitrary interval vol.62, pp.2, 2013, https://doi.org/10.1007/s12215-013-0121-y
  2. Approximating fixed points for continuous functions on an arbitrary interval vol.2013, pp.1, 2013, https://doi.org/10.1186/1029-242X-2013-214