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

In this paper, we introduce the new iterative sequences with errors approximating the common fixed point for a couple of quasi-contractive mappings and show the stability of the iterative procedures with errors in q-uniformly smooth Banach spaces. Our results extend, improve and unify the corresponding results of Chidume, Osilike, Liu, and others.

[1]  S. Ishikawa.  Fixed points by a new iteration method , 1974 .

[2]  Lishan Liu,et al.  Ishikawa and Mann Iterative Process with Errors for Nonlinear Strongly Accretive Mappings in Banach Spaces , 1995 .

[3]  B. Rhoades,et al.  A comparison of various definitions of contractive mappings , 1977 .

[4]  Zhenyu Huang,et al.  Mann and Ishikawa iterations with errors for asymptotically nonexpansive mappings , 1999 .

[5]  L. Qihou.  The convergence theorems of the sequence of Ishikawa iterates for hemicontractive mappings , 1990 .

[6]  N. Huang,et al.  A perturbed iterative procedure for multivalued pseudo-contractive mappings and multivalued accretive mappings in Banach spaces , 1999 .

[7]  Shih-sen Chang.  Random fixed point theorem in probabilistic analysis , 1981 .

[8]  Byung-Soo Lee,et al.  Convergence of iterative processes with errors for set-valued pseudocontractive and accretive type mappings in Banach spaces , 2000 .

[9]  L. Ciric,et al.  A generalization of Banach’s contraction principle , 1974 .

[10]  Liu Qihou,et al.  On Naimpally and Singh's open questions , 1987 .

[11]  Yuguang Xu,et al.  Ishikawa and Mann Iterative Processes with Errors for Nonlinear Strongly Accretive Operator Equations , 1998 .

[12]  Alberta Marie Harder,et al.  Fixed point theory and stability results for fixed point iteration procedures , 1987 .

[13]  Ravi P. Agarwal,et al.  STABILITY OF ITERATIVE PROCESSES WITH ERRORS FOR NONLINEAR EQUATIONS OF φ-STRONGLY ACCRETIVE TYPE OPERATORS , 2001 .

[14]  C. Chidume,et al.  FIXED POINT ITERATIONS FOR QUASI-CONTRACTIVE MAPS IN UNIFORMLY SMOOTH BANACH SPACES , 1993 .