We suggest a explicit viscosity iterative algorithm for nding a common el- ement of the set of common fixed points for W-mappings which solves some variational inequality. Also, we prove a strong convergence theorem with some control conditions. Finally, examples and numerical results are also given.

Article Title [Persian]

Viscosity Approximation Methods for
W-mappings in Hilbert space

Authors [Persian]

H. R. Sahebi^{1}; S. Ebrahimi^{2}

^{1}Department of Mathematics, Ashtian Branch, Islamic Azad University,
Ashtian, Iran.

^{2}Department of Mathematics, Ashtian Branch, Islamic Azad University,
Ashtian, Iran.

Abstract [Persian]

We suggest a explicit viscosity iterative algorithm for nding a common el- ement of the set of common fixed points for W-mappings which solves some variational inequality. Also, we prove a strong convergence theorem with some control conditions. Finally, examples and numerical results are also given.

[1] E. Blum and W. Oettli, From optimization and variational inequalities to equilibrium problems, Math Stud. 63 (1994), 123{145. [2] S. chang, J. Lee and H. Chan, An new method for solving equilibrium problem xed point problem and variational inequality problem wiyh application to optimization, Nonlinear Anal. 70 (2009), 3307{3319. [3] Pl. Combettes and A. Histoaga, Equilibrium programming in Hilbert spaces, J. Nonlinear Convex Anal. 6 (2005), 117{136. [4] A. Mouda and M. Thera, Proximal and Dynamical Approaches to Equilibrium Problems, Lecture Notes in Economics and Mathematical Systems. 477 (1999), 187{201. [5] G. Marino and H.K. Xu, A Genaral iterative method for nonexpansive mappings in Hilbert spaces, J. Math. Ana. Appl. 318 (2006), 43{52. [6] Z. Opial, Weak convergence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 591{597. [7] X. Qin, Y. J. Cho and S. M. Kang, An iterative method for an innite family of nonexpansive mappings in Hilbert spaces,Bull. Malays. Math. Sci. Soc. 2 32(2) (2009), 161{171.

[8] K. Shimoji and W. Takahashi, Strong convergence to common xed points of innite nonexpansive mappings and applications, Taiwanese J. Math. 5(2) (2001), 387{404. [9] T. Suzuki, Strong convergence of Krasnoselkii and Manns type sequences for one-parameter nonexpansive semigroups without Bochner integrals, J. Math. Anal. Appl. 305 (2005), 227{239. [10] W. Takahashi and K. Shimoji, Convergence theorems for nonexpansive mappings and feasibility problems, Mathematical and Computer Modelling 32 (11-13) (2000), 1463{1471. [11] H. K. Xu, Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl. 298 (2004), 279{291.