A general iterative method for hierarchical variational inequality problems in Hilbert spaces and applications

Positivity - Tập 16 Số 3 - Trang 429-453 - 2012
Lai-Jiu Lin1, Wataru Takahashi1,2
1NATIONAL CHANGHUA UNIVERSITY OF EDUCATION

Tóm tắt

Từ khóa


Tài liệu tham khảo

Aoyama K., Kimura Y., Takahashi W.: Maximal monotone operators and maximal monotone functions for equilibrium problems. J. Convex Anal. 15, 395–409 (2008)

Aoyama K., Kimura Y., Takahashi W., Toyoda M.: Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space. Nonlinear Anal. 67, 2350–2360 (2007)

Aoyama K., Kimura Y., Takahashi W., Toyoda M.: On a strongly nonexpansive sequence in Hilbert spaces. J. Nonlinear Convex Anal. 8, 471–489 (2007)

Blum E., Oettli W.: From optimization and variational inequalities to equilibrium problems. Math. Student 63, 123–145 (1994)

Browder F.E.: Convergence theorems for sequences of nonlinear operators in Banach spaces. Math. Z. 100, 201–225 (1967)

Browder F.E., Petryshyn W.V.: Construction of fixed points of nonlinear mappings in Hilbert spaces. J. Math. Anal. Appl. 20, 197–228 (1967)

Combettes P.L., Hirstoaga S.A.: Equilibrium programming in Hilbert spaces. J. Nonlinear Convex Anal. 6, 117–136 (2005)

Eshita K., Takahashi W.: Approximating zero points of accretive operators in general anach spaces. JP J. Fixed Point Theory Appl. 2, 105–116 (2007)

Halpern B.: Fixed points of nonexpanding maps. Bull. Am. Math. Soc. 73, 957–961 (1967)

Liu Y.: A general iterative method for equilibrium problems and strict pseudo-contractions in Hilbert spaces. Nonlinear Appl. 71, 4852–4861 (2009)

Marino G., Xu H.-K.: A general iterative method for nonexpansive mappings in Hilbert spaces. J. Math. Anal. Appl. 318, 43–52 (2006)

Marino G., Xu H.-K: Weak and strong convergence theorems for strich pseudo-contractions in Hilbert spaces. J. Math. Anal. Appl. 329, 336–346 (2007)

Moudafi A.: Viscosity approximation methods for fixed point problems. J. Math. Anal. Appl. 241, 46–55 (2000)

Moudafi A.: Weak convergence theorems for nonexpansive mappings and equilibrium problems. J. Nonlinear Convex Anal. 9, 37–43 (2008)

Nadezhkina N., Takahashi W.: Strong convergence theorem by hybrid method for nonexpansive mappings and Lipschitz-continuous monotone mappings. SIAM J. Optim. 16, 1230–1241 (2006)

Rockafellar R.T.: On the maximal monotonicity of subdifferential mappings. Pac. J. Math. 33, 209–216 (1970)

Takahashi S., Takahashi W.: Strong convergence theorem for a generalized equilibrium problem and a nonexpansive mapping in a Hilbert space. Nonlinear Anal. 69, 1025–1033 (2008)

Takahashi S., Takahashi W., Toyoda M.: Strong convergence theorems for maximal monotone operators with nonlinear mappings in Hilbert spaces. J. Optim. Theory Appl. 147, 27–41 (2010)

Takahashi W.: Nonlinear Functional Analysis. Yokohama Publishers, Yokohama (2000)

Takahashi, W.: Convex Analysis and Approximation of Fixed Points. Yokohama Publishers, Yokohama (2000) (Japanese)

Takahashi W.: Introduction to Nonlinear and Convex Analysis. Yokohama Publishers, Yokohama (2009)

Takahashi, W.: Strong convergence theorems for maximal and inverse-strongly monotone mappings in Hilbert spaces and applications (to appear)

Takahashi W., Toyoda M.: Weak convergence theorems for nonexpansive mappings and monotone mappings. J. Optim. Theory Appl. 118, 417–428 (2003)

Tian M.: A general iterative algorithm for nonexpansive mappings in Hilbert spaces. Nonlinear Anal. 73, 689–694 (2010)

Wittmann R.: Approximation of fixed points of nonexpansive mappings. Arch. Math. 58, 486–491 (1992)

Xu H.K.: Another control condition in an iterative method for nonexpansive mappings. Bull. Austral. Math. Soc. 65, 109–113 (2002)

Xu H.K.: An iterative approach to quadratic optimization. J. Optim. Theory Appl. 116, 659–678 (2003)

Zhou H.: Convergence theorems of fixed points fot k-strict pseudo-contractions in Hilbert spaces. Nonlinear Anal. 69, 456–462 (2008)