A new viscosity approximation method for common fixed points of a sequence of nonexpansive mappings with weakly contractive mappings in Banach spaces

Volume 9, Issue 6, pp 3920--3930 http://dx.doi.org/10.22436/jnsa.009.06.39

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 1346 Downloads
• 2079 Views

Authors

Wei-Qi Deng - School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China.

Abstract

By use of a new viscosity approximation method, we construct an explicit iterative algorithm for finding common fixed points of a sequence of nonexpansive mappings with weakly contractive mappings in the framework of Banach spaces. A strong convergence theorem is obtained for solving a kind of variational inequality problems. Our results improve and extend the corresponding ones of other authors with related interest.

Share and Cite

Keywords

• Viscosity approximation
• nonexpansive mappings with weakly contractive mappings
• common fixed points
• variational inequalities.

MSC

•  47H09
•  47H10
•  65J15
•  47J25

References

• [1] I. Y. Alber, S. Guerre-Delabriere, Principle of weakly contractive maps in Hilbert spaces, New results in operator theory and its applications, 7-22, Oper. Theory Adv. Appl., 98, Birkhuser, Basel (1997)


• [2] P. L. Lions, Two remarks on the convergence of convex functions and monotone operators, Nonlinear Anal., 2 (1978), 553-562.


• [3] M. O. Osilike, S. C. Aniagbosor, B. G. Akuchu, Fixed points of asymptotically demicontractive mappings in arbitrary Banach spaces, Panamer. Math. J., 12 (2002), 77-88.


• [4] A. Razani, S. Homaeipour , Viscosity approximation to common fixed points of families of nonexpansive mappings with weakly contractive mappings , Fixed Point Theory Appl., 2010 (2010), 8 pages.


• [5] B. E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal., 47 (2001), 2683-2693.


• [6] Y. Song, R. Chen, Iterative approximation to common fixed points of nonexpansive mapping sequences in reflexive Banach spaces, Nonlinear Anal., 66 (2007), 591-603.


• [7] W. Takahashi , Nonlinear functional analysis: fixed point Theory and its applications, Yokohama Pub- lishers, Yokohama (2000)


• [8] Z. B. Xu, G. F. Roach, Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces, J. Math. Anal. Appl., 157 (1991), 189-210.


• [9] I. Yamada, N. Ogura, Hybrid steepest descent method for the variational inequality problem over the fixed point set of certain quasi-nonexpansive mappings, Numer. Funct. Anal. Optim, 25 (2004), 619-655.


• [10] S. S. Zhang, X. R. Wang, H. W. J. Lee, C. K. Chan, Viscosity method for hierarchical fixed point and variational inequalities with applications, Appl. Math. Mech. (English Ed.), 32 (2011), 241-250.