Articles

NECESSARY AND SUFFICIENT CONDITION OF THE STRONG CONVERGENCE FOR TWO FINITE FAMILIES OF UNIFORMLY#br# L-LIPSCHITZIAN MAPPINGS

  • GU Feng
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  • Institute of Applied Mathematics and Department of Mathematics Hangzhou Teacher’s College, Hangzhou 310012, China

Received date: 2009-09-07

  Online published: 2011-09-20

Supported by

The present studies were supported by the National Natural Science Foun-dation of China (11071169), the Natural Science Foundation of Zhejiang Province (Y6110287).

Abstract

The purpose of this paper is to study necessary and sufficient condition for the strong convergence of a new parallel iterative algorithm with errors for two finite families of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in this paper
improve and extend the recent ones announced by [2–7].

Cite this article

GU Feng . NECESSARY AND SUFFICIENT CONDITION OF THE STRONG CONVERGENCE FOR TWO FINITE FAMILIES OF UNIFORMLY#br# L-LIPSCHITZIAN MAPPINGS[J]. Acta mathematica scientia, Series B, 2011 , 31(5) : 2058 -2066 . DOI: 10.1016/S0252-9602(11)60381-0

References

[1] Gobel K, Kirk W A. A fixed points theorem for asymptotically nonexpansive mappings. Proc Amer Math Soc, 1972, 35(1): 171–174

[2] Schu J. Iterative construction of fixed point of asymptotically nonexpansive mappings. J Math Anal Appl, 1991, 158(2): 407–413

[3] Chang S S. Some results for asymptotically pseudo-contractive mappings and asymptotically nonexpansive mappings. Proc Amer Math Soc, 2001, 129(3): 845–853

[4] Ofoedu E U. Strong convergence theorem for uniformly L-Lipschitzian asymptotically pseudocontractive mapping in a real Banach space. J Math Anal Appl, 2006, 321(2): 722–728

[5] Cho Y J, Kang J I, Zhou H Y. Approximating common fixed points of asymptotically nonexpansive mappings. Bull Korean Math Soc, 2005, 42(4): 661–670

[6] Zeng L C. On the iterative approximation for asymptotically pseudo-contractive mappings in uniformly smooth Banach spaces. Chin Ann Math, 2005, 26(2): 283–290 (in Chinese)

[7] Zeng L C. On the approximation of fixed points for asymptotically nonexpansive mappings in Banach spaces. Acta Math Sci, 2003, 23A(1): 31–37 (in Chinese)

[8] Petryshyn WV, A characterization of strict convexity of Banach spaces and other uses of duality mappings. J Funct Anal, 1970, 6(2): 282–291

[9] Moore C, Nnoli B V. Iterative solution of nonlinear equations involving set-valued uniformly accretive operators. Comput Math Appl, 2001, 42(1/2): 131–140

[10] Chao L C, Zhang S S. Viscosity approximation methods for common fixed points of infinite nonexpansive nonself-mappings. Acta Math Sci, 2010, 30A(4): 1144–1157 (in Chinese)

[11] Yang L P, Xie X S. Strong convergence of implicit iterative scheme with errors for nonlinear mappings. Acta Math Sci, 2010, 30A(4): 1062–1070 (in Chinese)

Outlines

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