273
Views
6
CrossRef citations to date
0
Altmetric
Articles

Strong convergence theorems for firmly nonexpansive-type mappings and equilibrium problems in Banach spaces

, &
Pages 483-497 | Received 05 Jul 2011, Accepted 19 Sep 2011, Published online: 21 Dec 2011

References

  • Alber , Y . 1994 . Generalized projection operators in Banach spaces: properties and applications, (Proceedings of the Israel Seminar Ariel) . Israel. Funct. Differ. Eqns , 1 : 1 – 21 .
  • Alber , Y . 1996 . “ Metric and generalized projection operators in Banach spaces: Properties and applications ” . In Theory and Applications of Nonlinear Operators of Accretive and Monotone Type , Edited by: Kartsatos , AG . 15 – 50 . New York : Marcel Dekker .
  • Blum , E and Oettli , W . 1994 . From optimization and variational inequalities to equilibrium problems . Math. Stud. , 63 : 123 – 145 .
  • Ceng , LC , Mastroeni , G and Yao , JC . 2009 . Hybrid proximal-point methods for common solutions of equilibrium problems and zeros of maximal monotone operators . J. Optim. Theory Appl. , 142 : 431 – 449 .
  • Ceng , LC , Schaible , S and Yao , JC . 2010 . Strong convergence theorems for maximal monotone operators in Banach spaces . Optimization , 59 : 807 – 819 .
  • Ceng , LC and Yao , JC . 2008 . Hybrid viscosity approximation schemes for equilibrium problems and fixed point problems of infinite many nonexpansive mappings . Appl. Math. Comput. , 198 : 729 – 741 .
  • Chen , JW and Wan , Z . 2011 . Existence of solutions and convergence analysis for a system of quasivariational inclusions in Banach spaces . J. Inequality Appl. , 49 : 1 – 14 .
  • Chen , JW , Wan , Z , Yuan , L and Zheng , Y . 2011 . Approximation of fixed points of weak Bregman relatively nonexpansive mappings in Banach spaces . Int. J. Math. Math. Sci. , 2011 : 1 – 23 .
  • Chidume , CE , Khumalo , M and Zegeye , H . 2003 . Generalized projection and approximation of fixed points of nonself maps . J. Approx. Theory , 120 : 242 – 252 .
  • Cioranesu , I . 1990 . Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems , Dordrecht : Kluwer .
  • Honda , T , Takahashi , W and Yao , JC . 2010 . Nonexpansive retractions onto closed convex cones in Banach spaces . Taiwanese J. Math. , 3 : 1023 – 1046 .
  • Kamimura , S , Kohsaka , F and Takahashi , W . 2004 . Weak and strong convergence theorem for maximal monotone operators in a Banach space . Set-Valued Anal. , 12 : 417 – 429 .
  • Kamimura , S and Takahashi , W . 2003 . Strong convergence of a proximal-type algorithm in a Banach space . SIAM J. Optim. , 13 : 938 – 945 .
  • Kohsaka , F and Takahashi , W . 2004 . Strong convergence of an iterative sequence for maximal monotone operators in a Banach space . Abstr. Appl. Anal. , 3 : 239 – 249 .
  • Li , J . 2005 . The generalized projection operator on reflexive Banach spaces and its applications . J. Math. Anal. Appl. , 306 : 55 – 71 .
  • Li , L and Song , W . 2008 . Modified proximal-point algorithm for maximal monotone operators in Banach spaces . J. Optim. Theory Appl. , 138 : 45 – 64 .
  • Nakajo , K and Takahashi , W . 2003 . Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups . J. Math. Anal. Appl. , 279 : 372 – 379 .
  • Nilsrakoo , W and Saejung , S . 2008 . Strong convergence to common fixed points of countable relatively quasi-nonexpansive mappings . Fixed Point Theory Appl. , 2008 : 1 – 19 .
  • Reich , S . 1996 . “ A weak convergence theorem for the alternating method with Bregman distance ” . In Theory and Applications of Nonlinear Operators of Accretive and Monotone Type , Edited by: Kartsatos , AG . 313 – 318 . New York : Marcel Dekker .
  • Takahashi , W . 2000 . Nonlinear Functional Analysis-Fixed Point Theory and its Applications , Yokohama, Japan : Yokohama Publishers .
  • Takahashi , S and Takahashi , W . 2008 . Strong convergence theorems for a generalized equilibrium problem and a nonexpansive mapping in Hilbert space . Nonlinear Anal. , 69 : 1025 – 1033 .
  • Takahashi , W and Zembayashi , K . 2009 . Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces . Nonlinear Anal. , 70 : 45 – 57 .
  • Xu , HK . 1991 . Inequalities in Banach spaces with applications . Nonlinear Anal. , 16 : 1127 – 1138 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.