On the Problem of Nearest Common Fixed Point of Nonexpansive Mappings

ZHANG Shi-sheng

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ZHANG Shi-sheng. On the Problem of Nearest Common Fixed Point of Nonexpansive Mappings[J]. Applied Mathematics and Mechanics, 2006, 27(7): 775-780.

Citation:

ZHANG Shi-sheng. On the Problem of Nearest Common Fixed Point of Nonexpansive Mappings[J]. Applied Mathematics and Mechanics, 2006, 27(7): 775-780.

Citation:

ZHANG Shi-sheng. On the Problem of Nearest Common Fixed Point of Nonexpansive Mappings[J]. Applied Mathematics and Mechanics, 2006, 27(7): 775-780.

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On the Problem of Nearest Common Fixed Point of Nonexpansive Mappings

ZHANG Shi-sheng^1,2

1.
Department of Mathematics, Yibin University, Yibin, Sichuan 644007, P. R. China;

Received Date: 2004-12-03
Rev Recd Date: 2006-04-11
Publish Date: 2006-07-15

Abstract

Abstract

The purpose is by using the viscosity approximation method to study the cnvergence problem of the iterative scheme for an infinite family of onexpansive mappings and a given contractive mapping in a reflexive Banach space. Under suitable conditions, it was proved that the iterative sequence converges strongly to a common fixed point which was also the unique solution of some variational inequality in a reflexive Banach space. The results presented extend and improve some recent results.

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References(14)

References

[1]	Bauschke H H.The approximation of fixed points of compositions of nonexpansive mappings in Banach spaces[J].J Math Anal Appl,1996，202：150—159. doi: 10.1006/jmaa.1996.0308
[2]	Browder F E.Convergence of approximants to fixed points of nonexpansive nonlinear mappings in Banach spaces[J].Arch Rational Mech Anal,1967,24：82—90.
[3]	Chang S S.Viscosity approximation methods for a finite family of nonexpansive mappings in Banach spaces[EB].
[4]	Jung J S.Iterative approaches to common fixed points of nonexpansive mappings in Banach spaces[J].J Math Anal Appl,2005,302：509—520. doi: 10.1016/j.jmaa.2004.08.022
[5]	O'Hara J G,Pillay P,Xu H K.Iterative approaches to finding nearest common fixed point of nonexpansive mappings[J].Nonlinear Anal TMA,2003,54：1417—1426. doi: 10.1016/S0362-546X(03)00193-7
[6]	Song Y S,Chen R D,Zhou H Y.Viscosity approximation methods for nonexpansive nonself-mappings[J].J Math Anal Appl,2006,314：701—709. doi: 10.1016/j.jmaa.2005.04.018
[7]	Xu H K.Viscosity approximation methods for nonexpansive mappings[J].J Math Anal Appl,2004,298：279—291. doi: 10.1016/j.jmaa.2004.04.059
[8]	Shioji N,Takahashi W.Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces[J].Proc Amer Math Soc,1997,125：3641—3645. doi: 10.1090/S0002-9939-97-04033-1
[9]	Shimizu T,Takahashi W.Strong convergence to common fixed points of families of nonexpansive mappings[J].J Math Anal Appl,1997,211：71—83. doi: 10.1006/jmaa.1997.5398
[10]	Lim T C,Xu H K.Fixed point theories for asymptotically nonexpansive mappings[J].Nonlinear Anal TMA, 1994,22：1345—1355. doi: 10.1016/0362-546X(94)90116-3
[11]	Goebel K,Kirk W A.Topies in metric fixed point theory[J].Cambridge Studies in Advanced Mathematics,v 28,Cambridge University Press, 1990.
[12]	Chang S S.Some problems and results in the study of nonlinear analysis[J].Nonlinear Anal TMA,1997,30(7)：4197—4208. doi: 10.1016/S0362-546X(97)00388-X
[13]	Liu L S.Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive mappings in Banach spaces[J].J Math Anal Appl,1995,194:114—125. doi: 10.1006/jmaa.1995.1289
[14]	Bruck R E.On the convex approximation property and the asymptotic behavior of nonlinear contractions in Banach spaces[J].Israel J Math, 1981,38：304—314. doi: 10.1007/BF02762776