Iterative Methods for Generalized Split Feasibility Problems in Hilbert Spaces

Springer Science and Business Media LLC - Tập 23 Số 2 - Trang 205-221 - 2015
Wataru Takahashi1, Hong–Kun Xu2, Jen-Chin Yao1
1Department of Applied Mathematics, Kaohsiung Medical University, Kaohsiung, 80424, Taiwan
2Department of Applied Mathematics, Kaohsiung Medical University, Kaohsiung, Taiwan

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Tài liệu tham khảo

Barbu, V.: Nonlinear Semigroups and Differential Equations in Banach spaces, Translated from the Romanian, Editura Academiei Republicii Socialiste Romania, Bucharest. Noordhoff International Publishing, Leiden (1976)

Blum, E., Oettli, W.: From Optimization and Variational Inequalities to Equilibrium Problems. Math. Student 63, 123–145 (1994)

Byrne, C., Censor, Y., Gibali, A., Reich, S.: The Split Common Null Point Problem. J. Nonlinear Convex Anal 13, 759–775 (2012)

Censor, Y., Elfving, T.: A Multiprojection Algorithm Using Bregman Projections in a Product Space. Numer. Algorithm. 8, 221–239 (1994)

Censor, Y., Segal, A.: The Split Common Fixed-Point Problem for Directed Operators. J. Convex Anal 16, 587–600 (2009)

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

Cui, H., Wang, F.: Strong Convergence of the Gradient-Projection Algorithm in Hilbert Spaces. J. Nonlinear Convex Anal 14, 245–251 (2013)

Eshita, K., Takahashi, W.: Approximating Zero Points of Accretive Operators in General Banach Spaces, JP. JP. J. Fixed Point Theory Appl. 2, 105–116 (2007)

Igarashi, T., Takahashi, W., Tanaka, K.: Weak Convergence Theorems for Nonspreading Mappings and Equilibrium Problems. In: Akashi, S., Takahashi, W., Tanaka, T. (eds.) In Nonlinear Analysis and Optimization, pp 75–85. Yokohama Publishers, Yokohama (2008)

Iiduka, H., Takahashi, W.: Weak Convergence Theorem by Cesàro Means for Nonexpansive Mappings and Inverse-Strongly Monotone Mappings. J. Nonlinear Convex Anal 7, 105–113 (2006)

Kocourek, P., Takahashi, W., Yao, J.C.: Fixed Point Theorems and Weak Convergence Theorems for Genelalized Hybrid Mappings in Hilbert Spaces. Taiwan. J. Math 14, 2497–2511 (2010)

Kosaka, F., Takahashi, W.: Existence and Approximation of Fixed Points of Firmly Nonexpansive-Type Mappings in Banach Spaces. SIAM J.Optim. 19, 824–835 (2008)

Kosaka, F., Takahashi, W.: Fixed Point Theorems for a Class of Nonlinear Mappings Related to Maximal Monotone Operators in Banach Spaces. Arch. Math. (Basel) 91, 166–177 (2008)

Moudafi, A.: Weak Convergence Theorems for Nonexpansive Mappings and Equilibrium Problems. J. Nonlinear Convex Anal 9, 37–143 (2008)

Moudafi, A.: The Split Common Fixed Point Problem for Demicontractive Mappings. Inverse Probl. 26(055007), 6 (2010)

Moudafi, A., Théra, M.: Proximal and Dynamical Approaches to Equilibrium Problems. Springer 477, 187–201 (1999)

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)

Opial, Z.: Weak Covergence of the Sequence of Successive Approximations for Nonexpansive Mappings. Bull. Amer. Math. Soc. 73, 591–597 (1967)

Reich, S.: Weak Covergence Theorems for Nonexpansive Mappings in Banach Spaces. J. Math. Anal. Appl. 67, 274–276 (1979)

Rockafellar, R.T.: On The Maximal Monotonicity of Subdifferential Mappings. Pac. J. Math 33, 209–216 (1970)

Takahashi, S., Takahashi, W.: Viscosity Approximation Methods for Equilibrium Problems and Fixed Point Problems in Hilbert Spaces. J. Math. Anal. Appl. 331, 506–515 (2007)

Takahashi, S., Takahashi, W., Toyoda, M.t.: 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 (Japanese). Yokohama Publishers, Yokohama (2000)

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

Takahashi, W.: Fixed Point Theorems for New Nonlinear Mappings in a Hilbert Space. J. Nonlinear Convex Anal 11, 79–88 (2010)

Takahashi, W.: Strong Convergence Theorems for Maximal and Inverse-Strongly Monotone Mappings in Hilbert Spaces and Applications. J. Optim. Theory Appl. 157, 781–802 (2013)

Takahashi, W., Toyoda, M.: Weak Convergence Theorems for Nonexpansive Mappings and Monotone Mappings. J. Optim. Theory Appl. 118, 417–428 (2003)

Tan, K.K., Xu, H.K.: Approximating Fixed Points of Nonexpansive Mappings by the Ishikawa Iteration Process. J. Math. Anal. Appl. 178, 301–308 (1993)

Xu, H.K.: Another Control Condition in an Iterative Method for Nonexpansive Mappings. Bull. Austral. Math. Soc. 65, 109–113 (2002)

Xu, H.K.: Viscosity Approximation Methods for Nonexpansive Mappings. J. Math. Anal. Appl. 298, 279–291 (2004)

Xu, H.K.: A Variable Krasnosel’skii-Mann Algorithm and the Multiple-set Split Feasibility Problem. Inverse Probl. 22, 2021–2034 (2006)

Xu, H.K.: Averaged Mappings and the Gradient-Projection Algorithm. J. Optim. Theory Appl. 150, 360–378 (2011)