JOURNAL BROWSE
Search
Advanced SearchSearch Tips
WEAK AND STRONG CONVERGENCE FOR QUASI-NONEXPANSIVE MAPPINGS IN BANACH SPACES
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
WEAK AND STRONG CONVERGENCE FOR QUASI-NONEXPANSIVE MAPPINGS IN BANACH SPACES
Kim, Gang-Eun;
  PDF(new window)
 Abstract
In this paper, we first show that the iteration {} defined by converges strongly to some fixed point of T when E is a real uniformly convex Banach space and T is a quasi-nonexpansive non-self mapping satisfying Condition A, which generalizes the result due to Shahzad [11]. Next, we show the strong convergence of the Mann iteration process with errors when E is a real uniformly convex Banach space and T is a quasi-nonexpansive self-mapping satisfying Condition A, which generalizes the result due to Senter-Dotson [10]. Finally, we show that the iteration {} defined by converges strongly to a common fixed point of T and S when E is a real uniformly convex Banach space and T, S are two quasi-nonexpansive self-mappings satisfying Condition D, which generalizes the result due to Ghosh-Debnath [3].
 Keywords
weak and strong convergence;fixed point;Opial's condition;Condition A;Condition D;quasi-nonexpansive mapping;
 Language
English
 Cited by
1.
An algorithm for finding common solutions of various problems in nonlinear operator theory, Fixed Point Theory and Applications, 2014, 2014, 1, 9  crossref(new windwow)
2.
Convergence theorems of a new iteration for two nonexpansive mappings, Journal of Inequalities and Applications, 2014, 2014, 1, 82  crossref(new windwow)
3.
Modified Halpern-type iterative methods for relatively nonexpansive mappings and maximal monotone operators in Banach spaces, Fixed Point Theory and Applications, 2014, 2014, 1, 237  crossref(new windwow)
 References
1.
F. E. Browder, Semicontractive and semiaccretive nonlinear mappings in Banach spaces, Bull. Amer. Math. Soc. 74 (1968), 660-665. crossref(new window)

2.
W. G. Dotson, On the Mann iterative process, Trans. Amer. Math. Soc. 149 (1970), 65-73. crossref(new window)

3.
M. K. Ghosh and L. Debnath, Approximating common fixed points of families of quasinonexpansive mappings, Internat. J. Math. Math. Sci. 18 (1995), no. 2, 287-292. crossref(new window)

4.
C. W. Groetsch, A note on segmenting Mann iterates, J. Math. Anal. Appl. 40 (1972), 369-372. crossref(new window)

5.
S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc. 44 (1974), 147-150. crossref(new window)

6.
M. Maiti and M. K. Ghosh, Approximating fixed points by Ishikawa iterates, Bull. Austral. Math. Soc. 40 (1989), no. 1, 113-117. crossref(new window)

7.
W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506-510. crossref(new window)

8.
Z. Opial, Weak convergence of the sequence of successive approximations for nonexpan- sive mappings, Bull. Amer. Math. Soc. 73 (1967), 591-597. crossref(new window)

9.
J. Schu, Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. Austral. Math. Soc. 43 (1991), no. 1, 153-159. crossref(new window)

10.
H. F. Senter and W. G. Dotson, Approximating fixed points of nonexpansive mappings, Proc. Amer. Math. Soc. 44 (1974), 375-380. crossref(new window)

11.
N. Shahzad, Approximating fixed points of non-self nonexpansive mappings in Banach spaces, Nonlinear Anal. 61 (2005), no. 6, 1031-1039. crossref(new window)

12.
K. K. Tan and H. K. Xu, Approximating fixed points of nonexpansive mappings by the Ishikawa Iteration process, J. Math. Anal. Appl. 178 (1993), no. 2, 301-308. crossref(new window)

13.
Y. Xu, Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl. 224 (1998), no. 1, 91-101. crossref(new window)