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STRONG CONVERGENCE IN NOOR-TYPE ITERATIVE SCHEMES IN CONVEX CONE METRIC SPACES

이병수
한국수학교육학회|2015.05|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제22권 제2호|pp. 185-197

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참고문헌

키워드

convex structureconvex cone metric spaceNoor-type iterationf- expansive mappingasymptotically f-expansive mappingasymptotically quasi-f-expansive map- pingf-uniformly quasi-sup(f)-Lipschitzian mapping.
주제분류수학

초록

The author considers a Noor-type iterative scheme to approximate com- mon fixed points of an infinite family of uniformly quasi-sup(fn)-Lipschitzian map- pings and an infinite family of gn-expansive mappings in convex cone metric spaces. His results generalize, improve and unify some corresponding results in convex met- ric spaces [1, 3, 9, 16, 18, 19] and convex cone metric spaces [8].

Abstract

The author considers a Noor-type iterative scheme to approximate com- mon fixed points of an infinite family of uniformly quasi-sup(fn)-Lipschitzian map- pings and an infinite family of gn-expansive mappings in convex cone metric spaces. His results generalize, improve and unify some corresponding results in convex met- ric spaces [1, 3, 9, 16, 18, 19] and convex cone metric spaces [8].

참고문헌 (21)

  1. S.S. Chang, "Stronger convergence theorem for an infinite family of uniformly quasi-Lipschitzian mappings in convex metric spaces", Appl. Math. Comput, 217, pp.277~282 (2010)
  2. Y.J. Cho, "Weak and strong convengence theorems for three-step iteration with errors for asymptotically nonexpansive mappings", Comput. Math. Appl, 47, pp.707~717 (2004)
  3. Hafiz Fukhar-ud-din, "Convergence of iterates with errors of asymptotically quasi-nonexpansive mappings and applications", J. Math. Anal. Appl, 328, pp.821~829 (2007)
  4. L.-G. Huang, "Cone metric spaces and fixed point theorems of contractive mappings", J. Math. Anal. Appl, 322, pp.1468~1476 (2007)
  5. N.J. Huang, "Fixed point theorems of compatiable mappings in convex metric spaces", Soochow J. Math, 22, pp.439~447 (1996)
  6. A.R. Khan, "Convergence of a general iterative scheme for a finite family of asymptotically quasi-nonexpansive mappings in convex metric spaces and applications", Com. Math. Appl, 59(8), pp.2990~2995 (2010)
  7. A.R. Khan, "Common fixed points Noor iteration for a finite family of asymptotically quasi-nonexpansive mappings in Banach spaces", J. Math. Anal. Appl, 341, pp.1~11 (2008)
  8. B.-S. Lee, "Approximating common fixed points of two sequences of uniformly quasi-Lipschitziam mappings in convex cone metric spaces", Univ. J. Appl. Math, 1(3), pp.166~171 (2013)
  9. Q.Y. Liu, "Approximating the common fixed points of two se-quences of uniformly quasi-Lipschitzian mappings in convex metric spaces", Appl. Math. Comput, 216, pp.883~889 (2010)
  10. K. Nammanee, "The modified Noor iterations with errors for non-Lipschitzian mappings in Banach spaces", Appl. Math. Comput, 187, pp.669~679 (2007)
  11. M.A. Noor, "New approximation schemes for general variational inequalities", J. Math. Anal. Appl, 251, pp.217~229 (2000)
  12. M. A. Noor, "Some developments on general variational inequalities", Appl. Math. Comput, 152, pp.199~277 (2004)
  13. M.A. Noor, "Three-step methods for nonexpansive mappings and varia-tional inequalities", Appl. Math. Comput, 187, pp.680~685 (2007)
  14. S. Suantai, "Weak and strong convergence criteria of Noor iterations for asymptotically nonexpansive mappings", J. Math. Anal. Appl, 311, pp.506~517 (2005)
  15. W. Takahashi, "A convexity in metric space and nonexpansive mappings", Kodai. Math. Rep, 22, pp.142~149 (1970)
  16. Y.X. Tian, "Convergence of an Ishikawa type iterative scheme for asymptotically quasi-nonexpansive mappings", Comput. Math. Appl, 49, pp.1905~1912 (2005)
  17. Y.X. Tian, "Convergence theorems of three-step iterative scheme for a finite family of uniformly quasi-Lipschitzian mappings in convex metric spaces", Fixed Point Theory and Applications, pp.12~ (2009)
  18. C. Wang, "Convergence theorems for fixed points of uniformly quasi-Lipschizian mappings in convex metric spaces", Nonlinear Anal. TMA, 70, pp.2067~2071 (2009)
  19. C. Wang, "Approximating fixed points of a pair of contractive type mappings in generalized convex metric spaces", Appl. Math. Comput, 215, pp.1522~1525 (2009)
  20. B. Xu, "Fixed-point iterations for asymptotically nonexpansive mappings in Banach spaces", J. Math. Anal. Appl, 267, pp.444~453 (2002)
  21. Y. Yao, "Convergence of three-step iteration for asymptotically nonex-pansive mappings", Appl. Math. Comput, 187, pp.883~892 (2007)

관련 논문AI추천

Convergence of a new multistep iteration in convex cone metric spacesBirol Gunduz대한수학회 · 대한수학회논문집2017 · 제32권 제1호CONVERGENCE TO COMMON FIXED POINTS FOR A FINITE FAMILY OF GENERALIZED ASYMPTOTICALLY QUASI-NONEXPANSIVE MAPPINGS IN BANACH SPACESG. S. Saluja영남수학회 · East Asian Mathematical Journal2013 · 제29권 제1호COMMON FIXED POINTS OF ASYMPTOTICALLY NONEXPANSIVE MAPPINGS BY ONE-STEP ITERATION PROCESS IN CONVEX METRIC SPACES김종규, Mujahid Abbas, Safeer Hussain Khan영남수학회 · East Asian Mathematical Journal2010 · 제26권 제5호Convergence theorems of a finite family of asymptotically quasi-nonexpansive type mappings in Banach spacesGurucharan Singh Saluja영남수학회 · East Asian Mathematical Journal2011 · 제27권 제1호STRONG CONVERGENCE OF AN IMPLICIT ITERATION PROCESS FOR A FINITE FAMILY OF STRONG SUCCESSIVELY Φ-PSEUDOCONTRACTIVE MAPSQian Miao, Rudong Chen영남수학회 · East Asian Mathematical Journal2008 · 제24권 제1호Strong convergence for three classes of uniformly equi-continuous and asymptotically quasi-nonexpansive mappingsMeijuan Shang, Xiaolong Qin, Yongfu Su대한수학회 · 대한수학회지2008 · 제45권 제1호

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