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VISCOSITY APPROXIMATIONS FOR NONEXPANSIVE NONSELF-MAPPINGS IN BANACH SPACES

정종수
영남수학회 (Youngnam Mathematical Society)|2010.05|East Asian Mathematical Journal|제26권 제3호|pp. 337-350

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참고문헌

키워드

contractionvariational inequalityviscosity explicit iterative schemenonexpansive nonself-mappingweakly asymptotically regularstrictly convexweakly sequential continuous duality mapping
주제분류수학

초록

Strong convergence theorem of the explicit viscosity iterative scheme involving the sunny nonexpansive retraction for nonexpansive nonself-mappings is established in a reflexive and strictly convex Banach spaces having a weakly sequentially continuous duality mapping. The main result improves the corresponding result of [19] to the more general class of mappings together with certain different control conditions.

Abstract

Strong convergence theorem of the explicit viscosity iterative scheme involving the sunny nonexpansive retraction for nonexpansive nonself-mappings is established in a reflexive and strictly convex Banach spaces having a weakly sequentially continuous duality mapping. The main result improves the corresponding result of [19] to the more general class of mappings together with certain different control conditions.

참고문헌 (24)

  1. F. E. Browder, "Convergence theorems for sequences of nonlinear operators in Banach spaces", Math. Z., 100, pp.201~225 (1967)
  2. Y. J. Cho, "Some control conditions on iterative methods", Commun. Appl. Nonlinear Anal., 12(2), pp.27~34 (2005)
  3. I. Cioranescu, "Geometry of Banach spaces, Duality Mappings and Nonlinear Problems" (1990), Kluwer Academic Publishers
  4. K. Goebel, "Uniform Convexity, Hyperbolic Geometry and Nonexpansive Mappings" (1984), Marcel Dekker
  5. B. Halpern, "Fixed points of nonexpansive maps", Bull. Amer. Math. Soc., 73, pp.957~961 (1967)
  6. J. S. Jung, "Iterative schemes with some control conditions for a family of nite nonexpansive mappings in Banach space", Fixed Point Theory and Appl., 2005(2), pp.125~135 (2005)
  7. J. S. Jung, "Strong convergence of approximating xed points for nonex-pansive nonself-mappinfs in Banach spaces", Kodai Math. J., 21, pp.259~272 (1998)
  8. 정종수, "Convergence of approximating paths to solutions of variational inequalities involving non-Lipschitzian mappings", 대한수학회지, 45(2), pp.377~392 (2008), 대한수학회
  9. P. L. Lions, "Approximation de points xes de contractions", C. R. Acad. Sci. Ser A-B, Paris, 284, pp.1357~1359 (1977)
  10. L. S. Liu, "Iterative processes with errors for nonlinear strongly accretive mappings in Banach spaces", J. Math. Anal. Appl., 194, pp.114~125 (1995)
  11. G. Marino, "On approximating xed points for nonexpansive maps", Indian J. Math., 34, pp.91~98 (1992)
  12. S. Matsushita, "Strong convergence theorems for nonexpansive nonself-mappings without boundary conditions", Nonlinear Anal., 68, pp.412~419 (2008)
  13. C. H. Morales, "on the xed-point theory for local k-pseudocontractio", Proc. Amer. Math. Soc., 통권 : 81, pp.71~74 (1981)
  14. C. H. Morales, "Convergence of paths for pseudo-contractive mappings in Banach spaces", Proc. Amer. Math. Soc., 통권 : 128, pp.3411~3419 (2000)
  15. A. Mouda, "Viscosity approximation methods for xed-points problems", J. Math. Anal. Appl., 241, pp.46~55 (2000)
  16. J. G. O'Hara, "Iterative approaches to convex feasibity problems in Banach spaces", Nonlinear Anal., 64, pp.2022~2042 (2006)
  17. S. Reich, "Strong convergence theorems for resolvents of accretive operators in Banach spaces", J. Math. Anal. Appl., 75, pp.287~292 (1980)
  18. N. Shioji, "Strong convergence of approximated sequences for non-expansive mappings in Banach spaces", Proc. Amer. Math. Soc., 통권 : 125, pp.3641~3645 (1997)
  19. Y. Song, "Viscosity approximation methods for nonexpansive nonself-mappings", J. Math. Anal. Appl., 321, pp.316~326 (2006)
  20. R. Wittmann, "Approximation of xed points of nonexpansive mappings", Arch. Math., 59, pp.486~491 (1992)
  21. H. K. Xu, "Iterative algorithms for nonlinear operators", J. London Math. Soc., 66(2), pp.240~256 (2002)
  22. H. K. Xu, "Viscosity approximation methods for nonexpansive mappings", J. Math. Anal. Appl., 298, pp.279~291 (2004)
  23. H. K. Xu, "Strong convergence of an iterative method for nonexpansive and accretive op- erators", J. Math. Anal. Appl., 314, pp.631~634 (2006)
  24. H. K. Xu, "Strong convergence theorems for nonexpansive nonself- mappings", Nonlinear Anal., 24, pp.223~228 (1995)

관련 논문AI추천

CONVERGENCE OF VISCOSITY APPROXIMATIONS TO FIXED POINTS OF NONEXPANSIVE NONSELF-MAPPINGS IN BANACH SPACES정종수영남수학회 · East Asian Mathematical Journal2008 · 제24권 제1호CONVERGENCE THEOREMS ON VISCOSITY APPROXIMATION METHODS FOR FINITE NONEXPANSIVE MAPPINGS IN BANACH SPACES정종수한국수학교육학회 · 이론수학과 교직수학2009 · 제16권 제1호STRONG CONVERGENCE OF GENERAL ITERATIVE ALGORITHMS FOR NONEXPANSIVE MAPPINGS IN BANACH SPACES정종수대한수학회 · 대한수학회지2017 · 제54권 제3호Viscosity methods of approximation for a common solution of a finite family of accretive operatorsJun-Min Chen, Li-Juan Zhang, Tie-Gang Fan영남수학회 · East Asian Mathematical Journal2011 · 제27권 제1호Strong convergence of composite iterative methods for nonexpansive mappings정종수대한수학회 · 대한수학회지2009 · 제46권 제6호On iterative approximation of common fixed points of asymptotically nonexpansive mappings with applications김종규, 임원희, Xiaolong Qin영남수학회 · East Asian Mathematical Journal2012 · 제28권 제5호

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