CONVERGENCE THEOREMS OF A SCHEME WITH ERRORS FOR I-ASYMPTOTICALLY QUASI-NONEXPANSIVE MAPPINGS

Volume 3, Issue 3, pp 222-233 http://dx.doi.org/10.22436/jnsa.003.03.08

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Authors

SEYIT TEMIR - Department of Mathematics, Art and Science Faculty, Harran University, 63200, Sanliurfa, Turkey.

Abstract

In this paper, we prove weak and strong convergence of the Ishikawa iterative scheme with errors to common fixed point I-asymptotically quasi- nonexpansive mappings in a Banach space. The results obtained in this paper improve and generalize the corresponding results in the existing literature.

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Keywords

• I-asymptotically quasi-nonexpansive mapping
• Ishikawa iterative schemes
• convergence theorems.

MSC

•  47H09
•  47H10

References

• [1] M. K. Ghosh, L. Debnath , Convergence of Ishikawa iterates of quasi-nonexpansive mappings , J. Math. Anal. Appl. , 207 (1997), 96-103.


• [2] K. Goebel, W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 35 (1972), 171-174.


• [3] S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc., 44 (1974), 147-150.


• [4] H. Y. Lan, Common fixed point iterative processes with errors for generalized asymptotically quasi-nonexpansive mappings, Computers and Math. with Applications, 52 (2006), 1403-1412.


• [5] Q. H. Liu, Iterative sequences for asymptotically quasi-nonexpansive mappings with Error Member, J. Math. Anal. Appl., 259 (2001), 18-24.


• [6] Z. Opial, Weak convergence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc., 73 (1967), 591-597.


• [7] W. V. Petryshyn, T. E. Williamson, Strong and weak convergence of the sequence of successive approximations for quasi-nonexpansive mappings, J. Math. Anal. Appl., 43 (1973), 459-497.


• [8] B. E. Rhoades, S. Temir, Convergence theorems for I-nonexpansive mapping, IJMMS, Article ID 63435, 2006 (2006), 1-4.


• [9] J. Schu, Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bulletin of the Australian Mathematical Society, 43 (1991), 153-159.


• [10] N. Shahzad, A. Udomene, Apprximating common fixed points of two asymptotically quasi-nonexpansive mappings in Banach spaces, Fixed Point Theory and Applications, Article ID18909, 2006 (2006), 1-10.


• [11] K. K. Tan, H. K. Xu, Approximating fixed points of nonexpansive mappings by the Ishikawa iterative process, J. Math. Anal. Appl., 178 (1993), 301-308.


• [12] S. Temir, O. Gul, Convergence theorem for I-asymptotically quasi-nonexpansive mapping in Hilbert space, J. Math. Anal. Appl., 329 (2007), 759-765.


• [13] S. S. Yao, L. Wang, Strong convergence theorems for I-quasi-nonexpansive mappings, Far east J. Math.Sci.(FJMS), 27 (1) (2007), 111-119.