Strong convergence of a new composite iterative method for equilibrium problems and fixed point problems

In this paper, we propose a new composite iterative method for finding a common point of the set of solutions of an equilibrium problem and the set of fixed points of a countable family of nonexpansive mappings in a Hilbert space. It is proved that the sequence generated by the iterative scheme converges strongly to a common point of the set of solutions of an equilibrium problem and the set of fixed points of a countable family of nonexpansive mappings. Our results improve and extend the corresponding ones announced by many others.

[1]  Jong Soo Jung Strong convergence of composite iterative methods for equilibrium problems and fixed point problems , 2009, Appl. Math. Comput..

[2]  Satit Saejung,et al.  Strong Convergence to Common Fixed Points of Countable Relatively Quasi-Nonexpansive Mappings , 2008 .

[3]  W. Oettli,et al.  From optimization and variational inequalities to equilibrium problems , 1994 .

[4]  Somyot Plubtieng,et al.  A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces , 2007 .

[5]  J. Jung Convergence on Composite Iterative Schemes for Nonexpansive Mappings in Banach Spaces , 2008 .

[6]  Giuseppe Marino,et al.  A general iterative method for nonexpansive mappings in Hilbert spaces , 2006 .

[7]  Wataru Takahashi,et al.  Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space , 2007 .

[8]  J. Jung Viscosity approximation methods for a family of finite nonexpansive mappings in Banach spaces , 2006 .

[9]  Z. Opial Weak convergence of the sequence of successive approximations for nonexpansive mappings , 1967 .

[10]  P. L. Combettes,et al.  Equilibrium programming in Hilbert spaces , 2005 .

[11]  Jong Soo Jung,et al.  STRONG CONVERGENCE OF COMPOSITE ITERATIVE METHODS FOR NONEXPANSIVE MAPPINGS , 2009 .

[12]  J. Jung CONVERGENCE THEOREMS OF ITERATIVE ALGORITHMS FOR A FAMILY OF FINITE NONEXPANSIVE MAPPINGS , 2007 .

[13]  Jen-Chih Yao,et al.  A viscosity approximation scheme for system of equilibrium problems, nonexpansive mappings and monotone mappings , 2009 .

[14]  J. Jung Convergence of composite iterative methods for finding zeros of accretive operators , 2009 .

[15]  Soon-Mo Jung,et al.  A Fixed Point Approach to the Stability of Quadratic Functional Equation with Involution , 2008 .

[16]  L. Ceng,et al.  Strong convergence of composite iterative schemes for zeros of m-accretive operators in Banach spaces , 2009 .