Skip to main content Accessibility help
×
Home

STRONG CONVERGENCE OF SOME ALGORITHMS FOR λ-STRICT PSEUDO-CONTRACTIONS IN HILBERT SPACE

  • YONGHONG YAO (a1), YEONG-CHENG LIOU (a2) and GIUSEPPE MARINO (a3)

Abstract

Two algorithms have been constructed for finding the minimum-norm fixed point of a λ-strict pseudo-contraction T in Hilbert space. It is shown that the proposed algorithms strongly converge to the minimum-norm fixed point of T.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      STRONG CONVERGENCE OF SOME ALGORITHMS FOR λ-STRICT PSEUDO-CONTRACTIONS IN HILBERT SPACE
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      STRONG CONVERGENCE OF SOME ALGORITHMS FOR λ-STRICT PSEUDO-CONTRACTIONS IN HILBERT SPACE
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      STRONG CONVERGENCE OF SOME ALGORITHMS FOR λ-STRICT PSEUDO-CONTRACTIONS IN HILBERT SPACE
      Available formats
      ×

Copyright

Corresponding author

For correspondence; e-mail: gmarino@unical.it

Footnotes

Hide All

The first author was supported in part by the Colleges and Universities Science and Technology Development Foundation (20091003) of Tianjin, NSFC 11071279 and NSFC 71161001-G0105. The second author was supported in part by NSC 100-2221-E-230-012.

Footnotes

References

Hide All
[1]Bauschke, H., ‘The approximation of fixed points of compositions of nonexpansive mappings in Hilbert spaces’, J. Math. Anal. Appl. 202 (1996), 150159.
[2]Browder, F. E. and Petryshyn, W. V., ‘Construction of fixed points of nonlinear mappings in Hilbert spaces’, J. Math. Anal. Appl. 20 (1967), 197228.
[3]Ceng, L. C., Cubiotti, P. and Yao, J. C., ‘Strong convergence theorems for finitely many nonexpansive mappings and applications’, Nonlinear Anal. 67 (2007), 14641473.
[4]Chancelier, J. P., ‘Iterative schemes for computing fixed points of nonexpansive mappings in Banach spaces’, J. Math. Anal. Appl. 353 (2009), 141153.
[5]Chang, S. S., ‘Viscosity approximation methods for a finite family of nonexpansive mappings in Banach spaces’, J. Math. Anal. Appl. 323 (2006), 14021416.
[6]Cho, Y. J. and Qin, X., ‘Convergence of a general iterative method for nonexpansive mappings in Hilbert spaces’, J. Comput. Appl. Math. 228(1) (2009), 458465.
[7]Cui, Y. L. and Liu, X., ‘Notes on Browder’s and Halpern’s methods for nonexpansive maps’, Fixed Point Theory 10(1) (2009), 8998.
[8]Jung, J. S., ‘Iterative approaches to common fixed points of nonexpansive mappings in Banach spaces’, J. Math. Anal. Appl. 302 (2005), 509520.
[9]Kim, T. H. and Xu, H. K., ‘Strong convergence of modified Mann iterations’, Nonlinear Anal. 61 (2005), 5160.
[10]Lewicki, G. and Marino, G., ‘On some algorithms in Banach spaces finding fixed points of nonlinear mappings’, Nonlinear Anal. 71 (2009), 39643972.
[11]Liu, X. and Cui, Y., ‘Common minimal-norm fixed point of a finite family of nonexpansive mappings’, Nonlinear Anal. 73 (2010), 7683.
[12]Lopez, G., Martin, V. and Xu, H. K., ‘Perturbation techniques for nonexpansive mappings with applications’, Nonlinear Anal. Real World Appl. 10 (2009), 23692383.
[13]Mainge, P. E., ‘Approximation methods for common fixed points of nonexpansive mappings in Hilbert spaces’, J. Math. Anal. Appl. 325 (2007), 469479.
[14]Marino, G. and Xu, H. K., ‘Convergence of generalized proximal point algorithms’, Commun. Pure Appl. Anal. 3 (2004), 791808.
[15]Marino, G. and Xu, H. K., ‘Weak and strong convergence theorems for strict pseudocontractions in Hilbert spaces’, J. Math. Anal. Appl. 329 (2007), 336349.
[16]Moudafi, A., ‘Viscosity approximation methods for fixed-point problems’, J. Math. Anal. Appl. 241 (2000), 4655.
[17]Petrusel, A. and Yao, J. C., ‘Viscosity approximation to common fixed points of families of nonexpansive mappings with generalized contractions mappings’, Nonlinear Anal. 69 (2008), 11001111.
[18]Plubtieng, S. and Wangkeeree, R., ‘Strong convergence of modified Mann iterations for a countable family of nonexpansive mappings’, Nonlinear Anal. 70 (2009), 31103118.
[19]Reich, S., ‘Weak convergence theorems for nonexpansive mappings in Banach spaces’, J. Math. Anal. Appl. 67 (1979), 274276.
[20]Saeidi, S., ‘Iterative algorithms for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of families and semigroups of nonexpansive mappings’, Nonlinear Anal. 70(12) (2009), 41954208.
[21]Scherzer, O., ‘Convergence criteria of iterative methods based on Landweber iteration for solving nonlinear problems’, J. Math. Anal. Appl. 194 (1991), 911933.
[22]Shang, M., Su, Y. and Qin, X., ‘Three-step iterations for nonexpansive mappings and inverse-strongly monotone mappings’, J. Syst. Sci. Complex. 22(2) (2009), 333344.
[23]Shioji, N. and Takahashi, W., ‘Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces’, Proc. Amer. Math. Soc. 125 (1997), 36413645.
[24]Solodov, M. V. and Svaiter, B. F., ‘Forcing strong convergence of proximal point iterations in a Hilbert space’, Math. Program. Ser. A 87 (2000), 189202.
[25]Suzuki, T., ‘Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces’, Proc. Amer. Math. Soc. 135 (2007), 99106.
[26]Wu, D., Chang, S. S. and Yuan, G. X., ‘Approximation of common fixed points for a family of finite nonexpansive mappings in Banach space’, Nonlinear Anal. 63 (2005), 987999.
[27]Xu, H. K., ‘Iterative algorithms for nonlinear operators’, J. London Math. Soc. 66 (2002), 240256.
[28]Xu, H. K., ‘Another control condition in an iterative method for nonexpansive mappings’, Bull. Aust. Math. Soc. 65 (2002), 109113.
[29]Xu, H. K., ‘Iterative methods for constrained Tikhonov regularization’, Comm. Appl. Nonlinear Anal. 10(4) (2003), 4958.
[30]Xu, H. K., ‘Iterative methods for the split feasibility problem in infinite-dimensional Hilbert spaces’, Inverse Problems 26 (2010), 105018 (17pp).
[31]Yao, Y., Chen, R. and Xu, H. K., ‘Schemes for finding minimum-norm solutions of variational inequalities’, Nonlinear Anal. 72 (2010), 34473456.
[32]Yao, Y. and Liou, Y. C., ‘An implicit extragradient method for hierarchical variational inequalities’, Fixed Point Theory Appl. 2011 (2011), 697248 (11pp).
[33]Yao, Y., Liou, Y. C. and Chen, R., ‘A general iterative method for an infinite family of nonexpansive mappings’, Nonlinear Anal. 69 (2008), 16441654.
[34]Yao, Y. and Xu, H. K., ‘Iterative methods for finding minimum-norm fixed points of nonexpansive mappings with applications’, Optimization 60(6) (2011), 645658.
[35]Zegeye, H. and Shahzad, N., ‘Viscosity approximation methods for a common fixed point of finite family of nonexpansive mappings’, Appl. Math. Comput. 191 (2007), 155163.
[36]Zeng, L. C., Wong, N. C. and Yao, J. C., ‘Strong convergence theorems for strictly pseudo-contractive mappings of Browder-Petryshyn type’, Taiwanese J. Math. 10 (2006), 837849.
[37]Zeng, L. C. and Yao, J. C., ‘Implicit iteration scheme with perturbed mapping for common fixed points of a finite family of nonexpansive mappings’, Nonlinear Anal. 64 (2006), 25072515.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Keywords

MSC classification

Related content

Powered by UNSILO

STRONG CONVERGENCE OF SOME ALGORITHMS FOR λ-STRICT PSEUDO-CONTRACTIONS IN HILBERT SPACE

  • YONGHONG YAO (a1), YEONG-CHENG LIOU (a2) and GIUSEPPE MARINO (a3)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.