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The New Viscosity Approximation Methods for Nonexpansive Nonself-Mappings

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DOI: 10.4236/ijmnta.2016.52011    969 Downloads   1,180 Views  

ABSTRACT

In this paper, to find the fixed points of the nonexpansive nonself-mappings, we introduced two new viscosity approximation methods, and then we prove the iterative sequences defined by above viscosity approximation methods which converge strongly to the fixed points of nonexpansive nonself-mappings. The results presented in this paper extend and improve the results of Song-Chen [1] and Song-Li [2].

Cite this paper

Liu, C. and Song, M. (2016) The New Viscosity Approximation Methods for Nonexpansive Nonself-Mappings. International Journal of Modern Nonlinear Theory and Application, 5, 104-113. doi: 10.4236/ijmnta.2016.52011.

References

[1] Song, Y.S. and Chen, R.D. (2006) Viscosity Approximation Methods for Nonexpansive Nonself-Mappings. Journal of Mathematical Analysis and Applications, 321, 316-326.
[2] Song, Y.S. and Li, Q.C. (2007) Viscosity Approximation for Nonexpansive Nonself-Mappings in Reflexive Banach Space. J. Sys. Sci. and Math. Scis, 481-487. (In Chinese)
[3] Halpern, B. (1967) Fixed Points of Nonexpanding Maps. Bulletin of the American Mathematical Society, 73, 957-961.
http://dx.doi.org/10.1090/S0002-9904-1967-11864-0
[4] Kalinde, A.K. (1992) Fixed Points Ishikawa Iterations. Journal of Mathematical Analysis Applications, 600-606.
[5] Dotson, W.G. (1970) On the Mann Iterative Process. Transactions of the American Mathematical Society, 149, 65-73.
[6] Morales, C.H. and Jung, J.S. (2000) Convergence of Paths for Pseudo-Contractive Mappings in Banach Space. Proceedings of The American Mathematical Society, 128, 3411-3419.
http://dx.doi.org/10.1090/S0002-9939-00-05573-8
[7] Liu, L.S. (1995) Ishikawa and Mann Iterative Processes with Errors for Nonlinear Strongly Accretive Mapping in Banach Spaces. Journal of Mathematical Analysis and Applications, 194, 114-125.
http://dx.doi.org/10.1006/jmaa.1995.1289

  
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