본문 바로가기
KERD
논문KCI 등재

Strong convergence for three classes of uniformly equi-continuous and asymptotically quasi-nonexpansive mappings

Yongfu Su|Meijuan Shang|Xiaolong Qin
대한수학회 (The Korean Mathematical Society)|2008.01|대한수학회지 (Journal of the KMS)|제45권 제1호|pp. 29-40

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

uniformly convex Banach spaceasymptotically quasi-nonexpansive mappinguniformly Holder continuousuniformly equi-continuous
주제분류수학

초록

In this paper, we introduce a modified three-step iteration scheme with errors for three classes of uniformly equi-continuous and asymptotically quasi-nonexpansive mappings in the framework of uniformly convex Banach spaces. We then use this scheme to approximate a common fixed point of these mappings. The results obtained in this paper extend and improve the recent ones announced by Khan, Fukhar-ud-di, Zhou, Cho, Noor and some others.

Abstract

In this paper, we introduce a modified three-step iteration scheme with errors for three classes of uniformly equi-continuous and asymptotically quasi-nonexpansive mappings in the framework of uniformly convex Banach spaces. We then use this scheme to approximate a common fixed point of these mappings. The results obtained in this paper extend and improve the recent ones announced by Khan, Fukhar-ud-di, Zhou, Cho, Noor and some others.

참고문헌 (17)

  1. Y. J. Cho, "Weak and strong convergence theorems for threestep iterations with errors for asymptotically nonexpansive mappings", Computers & Mathematics with Applications, 47(4), pp.707~717 (2004)
  2. C. E. Chidume, "Fixed point iteration for pseudocontractive maps", Proceedings of the American Mathematical Society, 통권 : 127, pp.1163~1170 (1999)
  3. G. Das, "Fixed points of quasinonexpansive mappings", Indian Journal of Pure and Applied Mathematics, 17(11), pp.1263~1269 (1986)
  4. S. H. Khan, "Weak and strong convergence of a scheme with errors for two nonexpansive mappings", NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 61(8), pp.1295~1301 (2005)
  5. S. Ishikawa, "Fixed points by a new iteration method", Proceedings of the American Mathematical Society, pp.147~150 (1974)
  6. K. Goebel, "A fixed point theorem for asymptotically nonexpansive mappings", Proceedings of the American Mathematical Society, 통권 : 35, pp.171~174 (1972)
  7. S. H. Khan, "Approximating common fixed points of two asymptotically nonexpansive mappings", Scientiae Mathematicae Japonicae, 53(1), pp.143~148 (2001)
  8. L. S. Liu, "Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces", Journal of Mathematical Analysis and Applications, 194(1), pp.114~125 (1995)
  9. M. Maiti, "Approximating fixed points by Ishikawa iterates", Bulletin of the Australian Mathematical Society, 40(1), pp.113~117 (1989)
  10. M. R. Mann, "Mean value methods in iteration", Proceedings of the American Mathematical Society, 통권 : 4, pp.506~510 (1953)
  11. B. Xu, "Fixed-point iterations for asymptotically nonexpansive mappings in Banach spaces", Journal of Mathematical Analysis and Applications, 267(2), pp.444~453 (2002)
  12. J. Schu, "Weak and strong convergence to fixed points of asymptotically nonexpansive mappings", Bulletin of the Australian Mathematical Society, 43(1), pp.153~159 (1991)
  13. H. F. Senter, "Approximating fixed points of nonexpansive mappings", Proceedings of the American Mathematical Society, 통권 : 44, pp.375~380
  14. W. Takahashi, "Convergence theorems for a pair of nonexpansive mappings", Journal of Convex Analysis, 5(1), pp.45~56 (1998)
  15. K. K. Tan, "Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process", Journal of Mathematical Analysis and Applications, 178(2), pp.301~308 (1993)
  16. Y. Xu, "Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive operator equations", Journal of Mathematical Analysis and Applications, 224(1), pp.91~101 (1998)
  17. H. Y. Zhou, "On the iterative methods for nonlinear operator equations in Banach spaces", Pan-American Mathematical Journal, 14(4), pp.61~68 (2004)

관련 논문AI추천

Weak and strong convergence of three step iteration scheme with errors for non-self asymptotically nonexpansive mappings권영철, 정재욱강원경기수학회 · 한국수학논문집2014 · 제22권 제2호Strong 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 제3호Convergence theorems of a finite family of asymptotically quasi-nonexpansive type mappings in Banach spacesGurucharan Singh Saluja영남수학회 · East Asian Mathematical Journal2011 · 제27권 제1호CONVERGENCE THEOREMS OF MULTI-STEP ITERATIVE SCHEMES WITH ERRORS FOR ASYMPTOTICALLY QUASI-NONEXPANSIVE TYPE NONSELF MAPPINGS김종규, G. S. Saluja, Hemant Kumar Nashine영남수학회 · East Asian Mathematical Journal2010 · 제26권 제1호APPROXIMATING 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 제3호CONVERGENCE TO COMMON FIXED POINTS FOR A FINITE FAMILY OF GENERALIZED ASYMPTOTICALLY QUASI-NONEXPANSIVE MAPPINGS IN BANACH SPACESG. S. Saluja영남수학회 · East Asian Mathematical Journal2013 · 제29권 제1호

이 간행물의 다른 논문 (17건)

Elements of the KKM theory on abstract convex spaces박세희pp. 1-27Lorentzian surfaces with constant curvatures and transformations in the 3-dimensional Lorentzian space박준상pp. 41-61Holomorphic functions on the mixed norm spaces on the polydiscStevo Stevicpp. 63-78The initial-boundary-value problem of a generalized Boussinesq equation on the half lineRuying Xuepp. 79-95Integral representations in electrical impedance tomography using boundary integral operators권기운pp. 97-119
원문 보기