On generalized Ishikawa iteration process and nonexpansive mappings in Banach spaces

• Autorzy: Sahu D. R.
• Języki publikacji: EN

Słowa kluczowe

EN

nonexpansive mapping; Banach space; Opial's condition

PL

przestrzeń Banacha

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2003
• Tom: Vol. 36, nr 3
• Strony: 721--734
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

Sahu D. R.

• Department of Applied Mathematics, Shri Shankaracharya College of Engineering, Junwani, Bhilai - 490020, India

Bibliografia

• [1] A. Aksoy and M. A. Khamsi, Nonstandard Methods in Fixed Point Theory, Springer Verlag, New Yark, (1990).
• [2] F. E. Browder, Nonexpansive nonlinear operators and nonlinear equation of evolution in Banach spaces, Proc. Sympos. Pure Math. 18 (1976).
• [3] R. E. Bruck, A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces, Israel J. Math. 32 (1979), 107-116.
• [4] L. Deng, Convergence of the Ishikawa iteration process for nonexpansive mapping, J. Math. Anal. Appl. 199 (1996), 769-775.
• [5] G. Emmanuele, Convergence of the Mann-Ishikawa iterative process for nonexpansive mappings, Nonlinear Anal. 6 (1982), 1135-1141.
• [6] K. Goebel and W. A. Kirk, Topics in Metric Fixed Points Theory, Cambridge Univ. Press, Cambridge (1990).
• [7] K. S. Ha and J. S. Jung, Strong convergence theorem for accretive operators in Banach spaces, J. Math. Anal. Appl. 147 (1990), 330-339.
• [8] S. Ishikawa, Fixed points and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc. 59 (1976), 65-71.
• [9] J. S. Jung, Y. J. Cho and B. S. Lee, Asymptotic behavior of nonexpansive iterations in Banach spaces, Comm. Appl. Nonlinear Anal. 7 (2000), 63-76.
• [10] W. A. Kirk, A fixed point theorem for mappings which do not increase distance, Amer. Math. Monthly, 72 (1965), 1004-1006.
• [11] G. G. Lorentz, A contribution to the theory of divergent series, Acta. Math. 80 (1948), 167-190.
• [12] W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506-610.
• [13] Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mapping, Bull. Amer. Math. Soc. 73 (1967), 595-597.
• [14] B. K. Sharma and D. R. Sahu, Convergence of fixed point of asymptotically nonexpansive mappings, Bull. Cal. Math. Soc. Accepted.
• [15] K. K. Tan and H. K. Xu, Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl. 178 (1993), 301-308.
• [16] S. Reich, Weak convergence theorem for nonexpansive mappings in Banach spaces, J. Math. Anal. 67 (1979), 274-276.
• [17] B. E. Rhoades, Comments on two fixed point iteration methods, J. Math. Anal. Appl. 56 (1976), 741-750.
• [18] B. E. Rhoades, Some properties of Ishikawa iterates of nonexpansive mappings, Indian J. Pure Appl. Math. 26 (1995), 953-957.
• [19] J. Schu, Weak convergence to fixed point of asymptotically nonexpansive mappings in uniformly convex Banach spaces with a Frechet differentiable norm, Lehrestuhl C for Mathematics, Preprint No. 21 (1990.).
• [20] L. C. Zeng, A note on approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl. 226 (1998), 245-250.