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CONVERGENCE THEOREMS OF MULTI-STEP ITERATIVE SCHEMES WITH ERRORS FOR ASYMPTOTICALLY QUASI-NONEXPANSIVE TYPE NONSELF MAPPINGS

김종규|G. S. Saluja|Hemant Kumar Nashine
영남수학회 (Youngnam Mathematical Society)|2010.01|East Asian Mathematical Journal|제26권 제1호|pp. 81-93

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참고문헌

키워드

fixed pointmulti-step iteration scheme with errorsreal uniformly convex Banach space
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초록

In this paper, a strong convergence theorem of multi-step iterative schemes with errors for asymptotically quasi-nonexpansive type nonself mappings is established in a real uniformly convex Banach space. Our results extend the corresponding results of Wangkeeree [12], Xu and Noor [13], Kim et al.[1,6,7] and many others.

Abstract

In this paper, a strong convergence theorem of multi-step iterative schemes with errors for asymptotically quasi-nonexpansive type nonself mappings is established in a real uniformly convex Banach space. Our results extend the corresponding results of Wangkeeree [12], Xu and Noor [13], Kim et al.[1,6,7] and many others.

참고문헌 (13)

  1. S. S. Chang, "Approximating xed points of asymptotically quasi-nonexpansive type mappings by the Ishikawa iterative sequences with mixed errors", Dynamic Systems and Appl., 13(2), pp.179~186 (2004)
  2. C. E. Chidume, "Strong and weak convergence theorem for asymptotically nonexpansive mappings", J. Math. Anal. Appl., 280, pp.364~374 (2003)
  3. R. Glowinski, "Augemented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics" (1989), Siam Philadelphia
  4. K. Goebel, "A xed point theorem for asymptotically nonexpansive map-pings", Proc. Amer. Math. Soc., 통권 : 35, pp.171~174 (1972)
  5. S. Haubruge, "Convergence analysis and applications of the Glowinski Le Tallec splitting method for nding a zero of the sum of two maximal monotone operators", J. Optim. Theory Appl., 97, pp.645~673 (1998)
  6. J. K. Kim, "Convergence theorems of modied three-step iterative sequences with mixed errors for asymptotically quasi-nonexpansive mappings in Banach spaces", PanAmerican Math. Jour., 14(1), pp.45~54 (2004)
  7. J. K. Kim, "Convergence theorems of implicit iterative se-quences for a nite family of asymptotically quasi-nonexpansive type mappings", Nonlin-ear Analysis TMA, 71, pp.2839~2848 (2009)
  8. M. A. Noor, "New approximation scheme for general variational inequalities", J. Math. Anal. Appl., 251, pp.217~229 (2000)
  9. M. A. Noor, "Three-step iterative algorithms for multivalued quasi variational inclusions", J. Math. Anal. Appl., 255 (2001)
  10. G. S. Saluja, "Strong convergence theorems of three step iterative sequences with errors for asymptotically quasi-nonexpansive type nonself mappings", J. Advances Appl. Math., Anal., 2(1), pp.57~69 (2007)
  11. K. K. Tan, "Approximating xed points of nonexpansive mappings", J. Math. Anal. Appl., 178, pp.301~308 (1993)
  12. R. Wangkeeree, "Strong convergence theorems of three step iterations with errors for asymptotically quasi-nonexpansive nonself-mappings in Banach spaces", Thai J. Math., 2, pp.283~294 (2004)
  13. B. L. Xu, "Fixed point iterations for asymptotically nonexpansive map-pings in Banach spaces", J. Math. Anal. Appl., 267(2), pp.444~453 (2002)

관련 논문AI추천

Convergence theorems of a finite family of asymptotically quasi-nonexpansive type mappings in Banach spacesGurucharan Singh Saluja영남수학회 · East Asian Mathematical Journal2011 · 제27권 제1호Approximating Common Fixed Points of One-step Iterative Scheme with Error for Asymptotically Quasi-nonexpansive Type Nonself-MappingsNarongrit Puturong경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2009 · 제49권 제4호Weak and strong convergence of three step iteration scheme with errors for non-self asymptotically nonexpansive mappings권영철, 정재욱강원경기수학회 · 한국수학논문집2014 · 제22권 제2호Strong convergence for three classes of uniformly equi-continuous and asymptotically quasi-nonexpansive mappingsMeijuan Shang, Xiaolong Qin, Yongfu Su대한수학회 · 대한수학회지2008 · 제45권 제1호Strong Convergence Theorems by Modified Four Step Itera tive Scheme with Errors for Three Nonexpansive MappingsAmarjeet Singh Saluja, Pankaj Kumar Jhad경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2015 · 제55권 제3호APPROXIMATING COMMON FIXED POINTS OF ONE-STEP ITERATIVE SCHEME WITH ERROR FOR NON-SELF ASYMPTOTICALLY NONEXPANSIVE IN THE INTERMEDIATE SENSE MAPPINGSGurucharan Singh Saluja, Hemant Kumar Nashine영남수학회 · East Asian Mathematical Journal2010 · 제26권 제3호

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