References

STRONG CONVERGENCE OF MODIFIED MANN ITERATIONS FOR LIPSCHITZ PSEUDOCONTRACTIONS


[1] F. E. Browder, Fixed-point theorems for noncompact mappings in Hilbert space, Proc. Natl. Acad. Sci. USA 53 (1965), 1272-1276.

[2] R. E. Bruck, On the convex approximation property and the asymptotic behavior of nonlinear contractions in Banach spaces, Israel J. Math. 38 (1981), 304-314.

[3] R. E. Bruck, A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces, Israel J. Math. 32 (1979), 107-116.

[4] R. Chen, Y. Song and H. Zhou, Convergence theorems for implicit iteration process for a finite family of continuous pseudocontractive mappings, J. Math. Anal. Appl. 314 (2006), 701-709.

[5] R. Chen, Y. Song and H. Zhou, Viscosity approximation methods for continous pseudo-contractive mappings, Acta Mathematica Sinica, Chinese series 49 (2006), 1275-1278.

[6] C. E. Chidume and E. U. Ofoedu, A new iteration process for generalized Lipschitz pseudo-contractive and generalized Lipschitz accretive mappings, Nonlinear Anal. 67 (2007), 307-315.

[7] C. E. Chidume and C. O. Chidume, Iterative approximation of fixed points of nonexpansive mappings, J. Math. Anal. Appl. 318 (2006), 288-295.

[8] C. E. Chidume and S. A. Mutangadura, An example on the Mann iteration method for Lipschitz pseudocontractions, Proc. Amer. Math. Soc. 129(8) (2001), 2359-2363.

[9] C. E. Chidume and C. Moore, Fixed point iteration for pseudo-contractive maps, Proc. Amer. Math. Soc. 127(4) (1999), 1163-1170.

[10] C. E. Chidume, Global iteration schemes for strongly pseudo-contractive maps, Proc. Amer. Math. Soc. 126(9) (1998), 2641-2649.

[11] C. E. Chidume, Approximation of fixed points of strongly pseudo-contractive mappings, Proc. Amer. Math. Soc. 120(2) (1994), 545-551.

[12] C. E. Chidume, Iterative approximation of Lipschitz strictly pseudo-contractive mappings, Proc. Amer. Math. Soc. 99(2) (1987), 283-288.

[13] Y. J. Cho and X. Qin, Viscosity approximation methods for a family of m-accretive mappings in reflexive Banach spaces, Positivity (2008), DOI 10.1007/s11117-007-2181-8.

[14] K. Deimling, Zero of accretive operators, Manuscripta Math. 13 (1974), 365-374.

[15] L. Deng and X. P. Ding, Iterative approximation of Lipschitz strictly pseudo-contractive mappings in uniformly smooth Banach spaces, Nonlinear Anal. 24(7) (1995), 981-987.

[16] L. Deng, On chidumes open problems, J. Math. Anal. Appl. 174(2) (1993), 441-449.

[17] T. L. Hicks and J. R. Kubicek, On the Mann iteration process in Hilbert space, J. Math. Anal. Appl. 59 (1977), 498-504.

[18] T. H. Kim and H. K. Xu, Strong convergence of modified Mann iterations, Nonlinear Anal. 61 (2005), 51-60.

[19] E. Kopecká and S. Reich, Nonexpansive retracts in Banach spaces, Banach Center Publications 77 (2007), 161-174.

[20] L. S. Liu, Ishikawa and Mann iteration process with errors for nonlinear strongly accretive mappings in Banach spaces, J. Math. Anal. Appl. 194 (1995), 114-125.

[21] W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506-510.

[22] C. H. Morales and J. S. Jung, Convergence of paths for pseudo-contractive mappings in Banach spaces, Proc. Amer. Math. Soc. 128 (2000), 3411-3419.

[23] S. Reich, Strong convergence theorems for resolvents of accretive operators in Banach spaces, J. Math. Anal. Appl. 75 (1980), 287-292.

[24] S. Reich, Weak convergence theorems for nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 67 (1979), 274-276.

[25] S. Reich, Approximating zeros of accretive operators, Proc. Amer. Math. Soc. 51 (1975), 381-384.

[26] S. Reich, Asymptotic behavior of contractions in Banach spaces, J. Math. Anal. Appl. 44 (1973), 57-70.

[27] J. Schu, Approximating fixed points of Lipschitzian pseudocontractive mappings, Houston J. Math. 19 (1993), 107-115.

[28] Y. Song and S. Xu, Strong convergence theorems for nonexpansive semigroup in Banach spaces, J. Math. Anal. Appl. 338 (2008), 152-161.

[29] Y. Song and R. Chen, Strong convergence of an iterative method for non-expansive mappings, Mathematische Nachrichten 281(8) (2008), 1196-1204.

[30] Y. Song, A note on the paper A new iteration process for generalized Lipschitz pseudo-contractive and generalized Lipschitz accretive mappings, Nonlinear Anal. 68 (2008), 3047-3049.

[31] Y. Song, On a Mann type implicit iteration process for continuous pseudo-contractive mappings, Nonlinear Anal. 67 (2007), 3058-3063.

[32] Y. Song and R. Chen, Convergence theorems of iterative algorithms for continuous pseudo-contractive mappings, Nonlinear Anal. 67 (2007), 486-497.

[33] Y. Song and R. Chen, An approximation method for continuous pseudocontractive mappings, J. Inequal. Appl. (2006), 1-9.

[34] T. Suzuki, Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces, Proc. Amer. Math. Soc. 135 (2007), 99-106.

[35] T. Suzuki, Strong convergence theorems for infinite families of nonexpansive mappings in general Banach spaces, Fixed Point Theory and Applications 2005(1) (2005), 103-123.

[36] W. Takahashi and Y. Ueda, On Reich’s strong convergence for resolvents of accretive operators, J. Math. Anal. Appl. 104 (1984), 546-553.

[37] A. Udomene, Path convergence, approximation of fixed points and variational solutions of Lipschitz pseudocontractions in Banach spaces, Nonlinear Anal. 67 (2007), 2403-2414.

[38] H. K. Xu, Iterative algorithms for nonlinear operators, J. London Math. Soc. 66 (2002), 240-256.

[39] H. K. Xu, Strong convergence of an iterative method for nonexpansive and accretive operators, J. Math. Anal. Appl. 314 (2006), 631-643.

[40] H. Zhou, Convergence theorems for strict pseudo-contractions in 2-uniformly smooth Banach spaces, Nonlinear Analysis (2007), doi:10.1016/ j.na.2007.09.009.