Strong convergence of averaged iteration for asymptotitcally non-expansive non-self mappings

• Autorzy: Bano N. , Mir N. A.
• Języki publikacji: EN

Abstrakty

EN

Let K be a non-empty, closed, convex subset of a real reflexive Banach space E, such that K is a sunny non-expansive retract of E. We introduce implicit and explicit averaged iteration schemes for asymptotically non-expansive non-self mapping T : K → E and obtain the strong convergence to the fixed point of T. Our results can be considered as extension to the results obtained in [3], [8], [1], [5], [4], [6].

Słowa kluczowe

EN

asymptotically non expansive non self mapping; averaged iteration; uniformly covex Banach space; weakly sequentially continuous duality map

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2010
• Tom: Vol. 43, nr 3
• Strony: 681--690
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Bano N.

autor

Mir N. A.

• Center for Advanced Studies in Pure and Applied Mathematics Bahauddin Zakariya University Multan 60800, Pakistan,

Bibliografia

• [1] S. Matsushita, D. Kuroiwa, Strong convergence of averaging iterations of nonexpansive non-self-mappings, J. Math. Anal. Appl. 294 (2004), 206–214.
• [2] S. Matsushita, W. Takahashi, Strong convergence theorem for nonexpansive non-self-mappings without boundary conditions, Nonlinear Anal. (2006), doi:10.1016/j.na. 2006.11.007.
• [3] Yisheng Song, Strong convergence of averaged iteration for asymptotically nonexpansive mappings, Appl. Math. Comput. 204 (2008), 854–861.
• [4] T. Shimizu, W. Takahashi, Strong convergence to common fixed points of families of nonexpansive mappings, J. Math. Anal. Appl. 211 (1997), 71–83.
• [5] N. Shioji, W. Takahashi, Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces, Proc. Amer. Math. Soc. 12 (1997), 3641–3645.
• [6] N. Shioji, W. Takahashi, Strong convergence of averaged approximants for asymptotically non-expansive mappings in Banach spaces, J. Approx. Theory 97 (1999), 53–64.
• [7] W. Takahashi, Nonlinear Functional Analysis Fixed Point Theory and its Applications, Yokohama Publishers Inc., Yokohama, 2000 (in Japanese).
• [8] R. Wangkeeree, Viscosity approximative methods to Cesa‘ro mean iterations for nonexpansive nonselfmappings in Banach spaces, Appl. Math. Comput. 201 (2008), 239–249.
• [9] H. K. Xu, Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl. 298 (2004), 279–291.