Strict pseud-contraction strong convergence theorems for strict pseud-contractions

• Autorzy: Qin X. , Su Y.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we prove two strong convergence theorems for strict pseudocontractions in Hilbert spaces by hybrid methods. Our results extend and improve the recent ones announced by Nakajo and Takahashi [K. Nakajo, W. Takahashi,. Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003), 372-379], Marino and Xu [G. Marino, H.K. Xu, Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces, J. Math. Anal. Appl. 329 (2007), 336-346], Martinez-Yanes and Xu [C. Martinez-Yanes, H.K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anai. 64 (2006), 2400-2411] and some others.

Słowa kluczowe

EN

Hilbert space; nonexpansive mapping; fixed point; strict pseudo-contraction

PL

przestrzeń Hilberta; odwzorowania nieekspansywne; punkt stały odwzorowania

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2008
• Tom: Vol. 30
• Strony: 137--149
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Qin X.

autor

Su Y.

• Department of Mathematics Tianjin Polytechnic University Tianjin 300160, China,

Bibliografia

• [1] C.E. Chidume, S.A. Mutangadura, An example on the Mann iteration method for Lipschitz pseudocontractions, Proc. Am. Math. Soc.129 (2001), 2359-2363.
• [2] A. Genel, J. Lindenstrass, An example concerning fixed points, Israel J. Math. 22 (1975), 81-86.
• [3] B. Halpern, fixed points of nonexpanding maps, Bull. Am. Math. Soc. 73 (1967), 957-961.
• [4] S. Ishikawa, Fixed points by a new iteration medthod, Proc. Am. Math. Soc. 44 (1974), 147-150.
• [5] T.H. Kim, H.K. Xu, Strong convergence of modified mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Anal. 64 (2006), 1140-1152.
• [6] P.L. Lions, Approximation de points fixes de contractions, C.R. Acad. Sci. Ser. A-B Paris 284 (1977), 1357-1359.
• [7] W.R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506-510.
• [8] C. Martinez-Yanes, H.K. Xu, Strong convergence of the CQ method for fixed point iteration processes Nonlinear Anal. 64 (2006), 2400-2411.
• [9] G. Marino, H.K. Xu, Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces, J. Math. Anal. Appl. 329 (2007), 336-346.
• [10] S. Matsushita, W. Takahashi, A strong convergence theorem for relatively non-expansive mappings in a Banach space. J. Approx. Theory 134 (2005), 257-266.
• [11] K. Nakajo, W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003), 372-379.
• [12] X. Qin, Y. Su, Strong convergence theorems for relatively nonexpansive mappings in a Banach space, Nonlinear Anal. 67 (2007), 1958-1965.
• [13] X. Qin, Y. Su, M. Shang, Strong convergence theorems for asymptotically nonexpansive mappings by hybrid methods, Kyungpook Math. J. 48, (2008), 133-142.
• [14] X. Qin, Y. Su, M. Shang, Strong convergence of the composite Halpern iteration J. Math. Anal. Appl. 339 (2008), 996-1002.
• [15] S. Reich, Weak convergence theorems for nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 67 (1979), 274-276.
• [16] S. Reich, Strong convergence theorems for resolvents of accretive operators in Banach spaces, J. Math. Anal. Appl. 75 (1980), 287-292.
• [17] N. Shioji, W. Takahashi, Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces, Proc. Am. Math. Soc. 125 (1997), 3641-3645.
• [18] Y. Su, X. Qin, Strong convergence of modified Ishikawa iterations for nonlinear mappings, Proc. Indian Acad. Sci. Math. Sci. 117 (2007), 97-107.
• [19] R. Wittmann, Approximation of fixed points of nonexpansive mappings, Arch. Math. 58 (1992), 486-491.
• [20] H.K. Xu, Iterative algorithms for nonlinear operator, J. London Math. Soc. 66 (2002), 240-256.
• [21] K.K. Tan, K.K. Xu, Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math.-Anal. Appl. 178 (1993), 301-308.