Previous |  Up |  Next


common fixed point; iteration; asymptotically nonexpansive mapping in the intermediate sense; uniformly convex Banach space
Some strong convergence theorems of common fixed points of asymptotically nonexpansive mappings in the intermediate sense are obtained. The results presented in this paper improve and extend the corresponding results in Huang, Khan and Takahashi, Chang, Schu, and Rhoades.
[1] R. E.  Bruck, T.  Kuczumow and S.  Reich: Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property. Colloq. Math. 65 (1993), 169–179. MR 1240164
[2] S. S.  Chang: On the approximation problem of fixed point for asymptotically nonexpansive mappings. Indian J.  Pure Appl. Math. 32 (2001), 1297–1307. MR 1875448
[3] K.  Goebel and W. A.  Kirk: A fixed point theorem for asymptotically nonexpansive mappings. Proc. Amer. Math. Soc. 35 (1972), 171–174. DOI 10.1090/S0002-9939-1972-0298500-3 | MR 0298500
[4] J.-C.  Huang: Convergence theorems of the sequence of iterates for a finite family of asymptotically nonexpansive mappings. Internat. J.  Math. Sci. 27 (2001), 653–662. DOI 10.1155/S0161171201007244 | MR 1870571 | Zbl 1020.47060
[5] W. A.  Kirk: Fixed point theorems for non-Lipschitzian mappings of asymptotically nonexpansive type. Israel J.  Math. 17 (1974), 339–346. DOI 10.1007/BF02757136 | MR 0346605 | Zbl 0286.47034
[6] S. H.  Khan and W.  Takahashi: Approximating common fixed points of two asymptotically nonexpansive mappings. Math. Japon. 53 (2001), 143–148. MR 1821609
[7] M. O.  Osilike and S. C.  Aniagbosor: Weak and strong convergence theorems for fixed points of asymptotically nonexpansive mappings. Math. Comput. Modelling 32 (2000), 1181–1191. DOI 10.1016/S0895-7177(00)00199-0 | MR 1791754
[8] L.  Qihou: Convergence theorems of the sequence of iterates for asymptotically demicontractive and hemicontractive mappings. Nonlinear Anal. 26 (1996), 1835–1842. DOI 10.1016/0362-546X(94)00351-H | MR 1382548 | Zbl 0861.47047
[9] B. E.  Rhoades: Fixed point iteration for certain nonlinear mappings. J.  Math. Anal. Appl. 183 (1994), 118–120. DOI 10.1006/jmaa.1994.1135 | MR 1273436
[10] J.  Schu: Weak and strong convergence to fixed points of asymptotically nonexpansive mappings. Bull. Austral. Math. Soc. 43 (1991), 153–159. DOI 10.1017/S0004972700028884 | MR 1086729 | Zbl 0709.47051
[11] K. K.  Tan and H. K.  Xu: Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process. J.  Math. Anal. Appl. 178 (1993), 301–308. DOI 10.1006/jmaa.1993.1309 | MR 1238879
[12] Y.  Xu: Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive operator equations. J.  Math. Anal. Appl. 224 (1998), 91–101. DOI 10.1006/jmaa.1998.5987 | MR 1632966
Partner of
EuDML logo