APPROXIMATION OF FIXED POINTS OF ASYMPTOTICALLY κ-STRICT PSEUDOCONTRACTIONS IN A BANACH SPACE

Abstract

APPROXIMATION OF FIXED POINTS OF ASYMPTOTICALLY κ-STRICT PSEUDOCONTRACTIONS IN A BANACH SPACE

Abstract

In this paper, weak convergence theorems of a finite family of asymptotically k-strict pseudo-contractions are established in the framework of 2-uniformly smooth and uniformly convex Banach spaces.

Keywords

• Asymptotically k-strict pseudo-contraction,Fixed point,Non-expansive mapping,Strictly pseudo-contractive mapping,Uniformly smooth Banach space,2000 AMS Classification: 47 H 09

References

1. Acedo, G. L. and Xu, H. K. Iterative methods for strict pseudo-contractions in Hilbert spaces, Nonlinear Anal. 67, 2258–2271, 2007.
2. Browder, F. E. and Petryshyn, W. V. Construction of fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl. 20, 197–228, 1967.
3. Goebel, K. and Kirk, W. A. A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 35, 171–174, 1972.
4. Kr¨uppel, M. On an inequality for nonexpansive mappings in uniformly convex Banach spaces, Rostock. Math. Kolloq. 51, 25–32, 1997.
5. Mann, W.R. Mean value methods in iteration, Proc. Amer. Math. Soc. 4, 506–510, 1953.
6. Marino, G. and Xu, H. K. Weak and strong convergence theorems for strict pseudo- contractions in Hilbert space, J. Math. Anal. Appl. 329, 336–346, 2007.
7. Osilike, M. O. and Shehu, Y. Explicit averaging cyclic algorithm for common fixed points of asymptotically strictly pseudocontractive maps, Appl. Math. Comput. 213, 548–553, 2009. [8] Osilike, M. O. and Shehu, Y. Explicit averaging cyclic algorithm for common fixed points of a finite family of asymptotically strictly pseudocontractive maps in Banach spaces, Comput. Math. Appl. 57, 1502–1510, 2009.
8. Qin, X., Cho, Y. J., Kang, S. M. and Shang, M. A hybrid iterative scheme for asymptotically image-strict pseudo-contractions in Hilbert spaces, Nonlinear Anal. 70, 1902–1911, 2009.

9. Qin, X. Approximation of a zero point of accretive operator in Banach spaces, J. Math. Anal. Appl. 329, 415–424, 2007. [11] Qihou, L. Convergence theorems of the sequence of iterates for asymptotically demicontrac- tive and hemicontractive mappings, Nonlinear Anal. 26, 1835–1842, 1996.
10. Reich, S. Weak convergence theorems for nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 67, 274–276, 1979.
11. Tan, K. K. and Xu, H. K. Approximating fixed points of nonexpansive mappings by the Ishikawaiteration process, J. Math. Anal. Appl. 178, 301–308, 1993.
12. Xu, H. K. Inequalities in Banach spaces with applications, Nonlinear Anal. 16, 1127–1138, 1991.