Stability of iterative procedures with errors for approximating common fixed points of a couple of q-contractive-like mappings in Banach spaces

摘要

Recently, Agarwal, Cho, Li and Huang [R.P. Agarwal, Y.J. Cho. J. Li. N.J. Huang. Stability of iterative procedures with errors approximating common fixed points for a couple of quasi-contractive mappings in q-uniformly smooth Banach spaces, J. Math. Anal. Appl. 272 (2002) 435-447] introduced the new iterative procedures with errors for approximating the common fixed point of a couple of quasi-contractive mappings and showed the stability of these iterative procedures with errors in Banach spaces. In this paper, we introduce a new concept of a couple of q-contractive-like mappings (q > 1) in a Banach space and apply these iterative procedures with errors for approximating the common fixed point of the couple of q-contractive-like mappings. The results established in this paper improve, extend and unify the corresponding ones of Agarwal, Cho, Li and Huang [R.P. Agarwal. Y.J. Cho. J. U N.J. Huang, Stability of iterative procedures with errors approximating common fixed points for a couple of quasi-contractive mappings in q-uniformly smooth Banach spaces. J. Math. Anal. Appl. 272 (2002) 435-447]. Chidume [C.E. Chidume, Approximation of fixed points of quasi-contractive mappings in L-p spaces. Indian J. Pure Appl. Math. 22 (1991) 273-386], Chidume and Osilike [C.E. Chidume, M.O. Osilike. Fixed points iterations for quasi-contractive maps in uniformly smooth Banach spaces, Bull. Korean Math. Soc. 30 (1993) 201-212], Liu [Q.H. Liu, On Naimpally and Singh's open questions. J. Math. Anal. Appl. 124 (1987) 157-164: Q.H. Liu. A convergence theorem of the sequence of Ishikawa iterates for quasi-contractive mappings, J. Math. Anal. Appl. 146 (1990) 301-305], Osilike [M.O. Osilike, A stable iteration procedure for quasi-contractive maps, Indian J. Pure Appl. Math. 27 (1996) 25-34; M.O. Osilike, Stability of the Ishikawa iteration method for quasi-contractive maps, Indian J. Pure Appl. Math. 28 (1997) 1251-1265] and many others in the literature. (c) 2005 Elsevier Inc. All rights reserved.