대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제40권3호
  • /
  • Pages.351-363
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  • 2003
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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SOME GENERAL CONVERGENCE PRINCIPLES WITH APPLICATIONS

  • Zhou, H.Y. (Department of Mathematics, Shijiazhuang Mechanical Engineering College) ;
  • Gao, G.L. (Department of Mathematics, Shijiazhuang Mechanical Engineering College) ;
  • Guo, G.T. (Department of Mathematics, Huabei Petroleum Education College) ;
  • Cho, Y.J. (Department of Mathematics Education, College of Education, Gyeongsang National University)
  • 발행 : 2003.08.01
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초록

In the present paper, some general convergence principles are established in metric spaces and then theses principles are applied to the convergence of the iterative sequences for approximating fixed points of certain classes of mappings. By virtue of our principles, most of the latest results obtained by several authors can be deduced easily.

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참고문헌

  1. Nova Science Publishers Iterative Methods for Nonlinear Operator Equations in Banach Spaces S.S.Chang;Y.J.Cho;H.Y.Zhou
  2. Nonlinear Anal. v.49 Convergence theorems for asymptotically pseudocontractive mappings C.E.Chidume https://doi.org/10.1016/S0362-546X(00)00240-6
  3. Math. Comput. Modeling v.34 Approximations for fixed points of Φ-hemicontractive mappings by the Ishikawa iterative process with mixed errors Y.J.Cho;H.Y.Zhou;S.M.Kang;S.S.Kim https://doi.org/10.1016/S0895-7177(01)00044-9
  4. J. Math. Anal. Appl. v.207 Convergence of Ishikawa iterates of quasi-non-expansive mappings M.K.Ghosh;L.Debnath https://doi.org/10.1006/jmaa.1997.5268
  5. Proc. Amer. Math. Soc. v.35 A fixed point theorem for asymptotically nonexpansive mappings K.Goebel;W.A.Kirk https://doi.org/10.2307/2038462
  6. Comment. Math. Univ. Carolin v.30 Weak convergence theorems for asymptotically nonexpansive mapping in uniformly convex Banach spaces J.Gornicki
  7. Israel. J. Math. v.17 Fixed point theorems for non-Lipschitzian mappings of asymptotically nonexpansive type W.A.Kirk https://doi.org/10.1007/BF02757136
  8. J. Math. Anal. Appl. v.259 Iterative sequences for asymptotically quasi-nonexpansive mappings Q.H.Liu https://doi.org/10.1006/jmaa.2000.6980
  9. J. Math. Anal. Appl. v.259 Iterative sequences for asymptotically quasi-nonexpansive mappings with error member https://doi.org/10.1006/jmaa.2000.7353
  10. J. Math. Res. Exposition v.20 Convergence theorems of iterative sequences for asymptotically non-expansive mapping in a uniformly convex Banach space Q.H.Liu;L.X.Xue
  11. Comput. Math. Appl. v.40 Weak and strong convergence theorems for fixed paints of pseudocontractions and solutions of monotone type operator equations M.O.Osilike;D.I.Igbokwe https://doi.org/10.1016/S0898-1221(00)00179-6
  12. J. Math. Anal. Appl. v.43 Strong and weak convergence of the sequence of successive approximations for quasi-nonexpansive mappings W.V.Petryshyn;T.E.Williamson https://doi.org/10.1016/0022-247X(73)90087-5
  13. J. Math. Anal. Appl. v.158 Iterative construction of fixed points of asymptotically nonexpansive mappings J.Schu https://doi.org/10.1016/0022-247X(91)90245-U
  14. Bull. Austral. Math. Soc. v.43 Weak and strong convergence to fixed points of asymptotically nonexpansive mappings https://doi.org/10.1017/S0004972700028884
  15. Proc. Amer. Meth. Soc. v.44 Approximating fixed points of non-expansive mappings H.F.Senter;W.G.Dotson,Jr. https://doi.org/10.1090/S0002-9939-1974-0346608-8
  16. J. Math. Anal. Appl. v.178 Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process K.K.Tan;H.K.Xu https://doi.org/10.1006/jmaa.1993.1309
  17. Proc. Amer. Math. Soc. v.122 Fixed point iteration processes for asymptotically nonexpansive mappings https://doi.org/10.1090/S0002-9939-1994-1203993-5
  18. Nonlinear Anal. v.16 Existence and convergence for fixed points of mappings of asymptotically nonexpansive type H.K.Xu https://doi.org/10.1016/0362-546X(91)90201-B
  19. J. Math. Anal. Appl. v.224 Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive operator equations Y.G.Xu https://doi.org/10.1006/jmaa.1998.5987
  20. Nonliear functional analysis and its applications I E.Zeidler
  21. Abstr. Appl. Anal. v.1 Approximating the zeros of accretive operators by the Ishikawa iteration process H.Y.Zhou;Y.T.Jia https://doi.org/10.1155/S1085337596000073

피인용 문헌

  1. Strong Convergence of an Implicit Algorithm in CAT(0) Spaces vol.2011, 2011, https://doi.org/10.1155/2011/173621
  2. A Note on “Common Fixed Point of Multistep Noor Iteration with Errors for a Finite Family of Generalized Asymptotically Quasi-Nonexpansive Mappings” vol.2009, 2009, https://doi.org/10.1155/2009/283461
  3. CONVERGENCE THEOREMS FOR GENERALIZED I-ASYMPTOTICALLY NONEXPANSIVE MAPPINGS IN A HADAMARD SPACES vol.31, pp.3, 2016, https://doi.org/10.4134/CKMS.c150167
  4. Convergence of three-step iterations for asymptotically nonexpansive mappings vol.187, pp.2, 2007, https://doi.org/10.1016/j.amc.2006.09.008
  5. Weak and strong convergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings vol.47, pp.4-5, 2004, https://doi.org/10.1016/S0898-1221(04)90058-2