Convergence of Three- Step Mean Value Iterative Scheme for a Mapping of Asymptotically Quasi - Nonexpansive Type
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Keywords:
asymptotically quasi - nonexpansive type completely continuous uniformly convex Banach space three - step mean value iterative scheme
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Abstract
In this paper, convergences of three- step mean value iterative scheme are established for a mapping ofasymptotically quasi – nonexpansive type in a uniformly convex Banach space. The results obtained in thispaper extend and improve the recent ones announced by D. R. Sahu and J. S. Jung [ Sahu and Jung, (2003) Fixed– point iteration processes for non- Lipschitzian mappings of asymptotically quasi- nonexpansive type,International Journal of Mathematics and Mathematical Sciences 2003 : 2075 - 2081], and many others.
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How to Cite
Puturong, N. (2013). Convergence of Three- Step Mean Value Iterative Scheme for a Mapping of Asymptotically Quasi - Nonexpansive Type. Science, Engineering and Health Studies, 2(1), 29–36. https://doi.org/10.14456/sustj.2008.3
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Research Articles
References
Megginson, Robert E. (1998). An Introduction to Banach Space Theory, Springer-Verlag New York, Inc.
Nilsrakoo, W. and Saejung, S. (2006). A new three-step fixed point iteration scheme for asymptotically nonexpansive mappings. Applied Mathematics and Computation, 181: 1026-1034.
Nilsrakoo, W. and Saejung, S. (2007). A reconsideration on convergence of three- step iterations for asymptotically nonexpansive mappings. Applied Mathematics and Computation, 190: 1472-1478.
Quan, J., Chang, S. S., and Long, X. J. (2006). Approximation common fixed point asymptotically quasi-nonexpansive type mappings by the finite steps iterative sequences. Fixed Point Theory and Applications, 2006: 1-8.
Sahu, D. R. and Jung, J. S. (2003). Fixed- point iteration processes for non- Lipschitzian mappings of asymptotically quasi - nonexpansivetype. International Journal of Mathematics and Mathematical Sciences, 2003: 2075-2081.
Schu, J. (1991). Iterative construction of fixed point of asymptotically nonexpansive mappings. Journal of Mathematical Analysis and Applications, 158: 407-413.
Schu, J. (1991). Weak and strong convergence of fixed points of asymptotically nonexpansive mappings. Bulletin of the Australian Mathematical Society, 43: 153-159.
Suantai, S. (2005). Weak and strong convergence criteria of Noor iterations for asymptotically nonexpansive mappings. Journal of Mathematical Analysis and Applications, 311: 506-517.
Tan, K. K. and Xu, H. K. (1993). Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process. Journal of Mathematical Analysis and Applications, 178: 301-308.
Xu, B. L. and Noor, M. A. (2002). Fixed point iterations for asymptotically nonexpansive mapping in Banach spaces. Journal of Mathematical Analysis and Applications, 267: 444-453.
Nilsrakoo, W. and Saejung, S. (2006). A new three-step fixed point iteration scheme for asymptotically nonexpansive mappings. Applied Mathematics and Computation, 181: 1026-1034.
Nilsrakoo, W. and Saejung, S. (2007). A reconsideration on convergence of three- step iterations for asymptotically nonexpansive mappings. Applied Mathematics and Computation, 190: 1472-1478.
Quan, J., Chang, S. S., and Long, X. J. (2006). Approximation common fixed point asymptotically quasi-nonexpansive type mappings by the finite steps iterative sequences. Fixed Point Theory and Applications, 2006: 1-8.
Sahu, D. R. and Jung, J. S. (2003). Fixed- point iteration processes for non- Lipschitzian mappings of asymptotically quasi - nonexpansivetype. International Journal of Mathematics and Mathematical Sciences, 2003: 2075-2081.
Schu, J. (1991). Iterative construction of fixed point of asymptotically nonexpansive mappings. Journal of Mathematical Analysis and Applications, 158: 407-413.
Schu, J. (1991). Weak and strong convergence of fixed points of asymptotically nonexpansive mappings. Bulletin of the Australian Mathematical Society, 43: 153-159.
Suantai, S. (2005). Weak and strong convergence criteria of Noor iterations for asymptotically nonexpansive mappings. Journal of Mathematical Analysis and Applications, 311: 506-517.
Tan, K. K. and Xu, H. K. (1993). Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process. Journal of Mathematical Analysis and Applications, 178: 301-308.
Xu, B. L. and Noor, M. A. (2002). Fixed point iterations for asymptotically nonexpansive mapping in Banach spaces. Journal of Mathematical Analysis and Applications, 267: 444-453.