Strong convergence of approximants to fixed points of asymptotically nonexpansive mappings in Banach spaces without uniform convexity

• Autorzy: Sahu, D. R. , Jung, J. S. , Cho, Y. J.
• Języki publikacji: EN

Słowa kluczowe

PL

różniczkowe normy Gateauxa; warunek Opiala

EN

asymptotically nonexpansive mapping; Gateaux differentiable norm; Opial's condition

• Czasopismo: Demonstratio Mathematica
• Rocznik: 2004
• Tom: Vol. 37, nr 2
• Strony: 419--428
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Sahu, D. R.

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

autor

Jung, J. S.

• Department of Mathematics, Dong-A University, Busan 604-714, Korea,

autor

Cho, Y. J.

• Department of Mathematics, Gyeongsang National University, Chiju 660-701, Korea,

Bibliografia

• [1] F. E. Browder, Convergence of approximants to fixed point of nonexpansive nonlinear mappings in Banach spaces, Arch. Rational Mech. Anal. 24 (1967), 82-90.
• [2] R. E. Bruck, Jr, Nonexpansive retracts of Banach spaces, Bull. Amer. Math. Soc. 76 (1970), 384-386.
• [3] J. P. Gossez and E. L. Dozo, Some geometric properties related to the fixed point theory for nonexpansive mappings, Pacific J. Math. 40 (1972), 565-573.
• [4} K. S. Ha and J. S. Jung, Strong convergence theorems for accretive operators in Banach spaces, J. Math. Anal. Appl. 147 (1990), 330-339.
• [5] J. S. Jung, D. R. Sahu, B. S. Thakur, Strong convergence theorems for asymptotically nonexpansive mappings in Banach spaces, Comm. Appl. Nonlinear Anal. 5 (1998), 53-69.
• [6] T. C. Lim and H. K. Xu, Fixed point theorem for asymptotically nonexpansive mapping, Nonlinear Anal. 22 (1994), 1345-1355.
• [7] Z. Opial, Weak convergence of the sequence of successive approximation for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 519-597.
• [8] S. Reich, Asymptotic behavior of contractions in Banach spaces, J. Math. Anal. Appl. 44 (1973), 57-70.
• [9] S. Reich, Strong convergence theorems for resolvents of accretive operators in Banach spaces, J. Math. Anal. Appl. 75 (1980), 287-292.
• [10] T. Shimizu and W. Takahashi, Strong convergence theorem for asymptotically nonexpansive mappings, Nonlinear Anal. 26 (1996), 265-272.
• [11] N. Shioji and W. Takahashi, Strong convergence of averaged approximants for nonexpansive mapping in Banach spaces, J. Approx. Theory, 97 (1999), 53-64.
• [12] W. Takahashi and Y. Ueda, On Reich's strong convergence theorems for resolvents of accretive operators, J. Math. Anal. Appl. 104 (1984), 546-553.