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Convergence Theorems of Mann and Ishikawa Iterative Processes with Errors for Multivalued Φ-strongly Accretive Mapping

Convergence Theorems of Mann and Ishikawa Iterative Processes with Errors for Multivalued Φ-strongly Accretive Mapping
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摘要 Let X be a real Banach space and A : X→ 2x a bounded uniformly continuous Φ-strongly accretive multivalued mapping. For any f ∈ X, Mann and Ishikawa iterative processes with errors converge strongly to the unique solution of Ax (?) f. The conclusion in this paper weakens the stronger conditions about errors in Chidume and Moore's theorem (J. Math. Anal. Appl, 245(2000), 142-160). Let X be a real Banach space and A : X→ 2x a bounded uniformly continuous Φ-strongly accretive multivalued mapping. For any f ∈ X, Mann and Ishikawa iterative processes with errors converge strongly to the unique solution of Ax (?) f. The conclusion in this paper weakens the stronger conditions about errors in Chidume and Moore's theorem (J. Math. Anal. Appl, 245(2000), 142-160).
作者 张国伟
出处 《Northeastern Mathematical Journal》 CSCD 2003年第2期174-180,共7页 东北数学(英文版)
关键词 Mann and Ishikawa iteration Φ-strongly accretive mapping conver-gence theorem Mann and Ishikawa iteration Φ-strongly accretive mapping conver-gence theorem
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参考文献6

  • 1Deimling, K., Nonlinear Functional Analysis, Springer-Verlag, Berlin/Heidelberg, 1985.
  • 2Chidume, C. E. and Moore, C., Steepest descent method for equilibrium points of nonlinear systems with accretive operators, J. Math. Anal. Appl., 245(2000), 142-160.
  • 3Liu L. S., Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive mappings in Banach spaces, J. Math. Anal. Appl., 194(1995), 114-125.
  • 4Xu Y., Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl., 224(1998), 91-101.
  • 5Liu Z. and Kang S. M., Convergence theorems for φ-strongly accretive and φ-hemicontractive operators, J. Math. Anal. Appl., 253(2001), 35-49.
  • 6Chang S. S., On Chidume's open questions and approximate solutions of multivalued strongly accretive mapping equations in Banach spaces, J. Math. Anal. Appl., 216(199),94-111.

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