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Hybrid projection algorithms for treating common fixed points of a family of demicontinuous pseudocontractions. (English) Zbl 1242.65112
Summary: A projection algorithm is considered for treating strongly continuous semigroups of demicontinuous pseudocontractions. Theorems of strong convergence of fixed points are established in the framework of real Hilbert spaces.

MSC:
65J15 Numerical solutions to equations with nonlinear operators (do not use 65Hxx)
47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47J15 Abstract bifurcation theory involving nonlinear operators
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[1] Xu, H.K.; Ori, M.G., An implicit iterative process for nonexpansive mappings, Numer. funct. anal. optim., 22, 767-773, (2001) · Zbl 0999.47043
[2] Reich, S., Weak convergence theorems for nonexpansive mappings in Banach spaces, J. math. anal. appl., 67, 274-276, (1979) · Zbl 0423.47026
[3] Genel, A.; Lindenstrass, J., An example concerning fixed points, Israel J. math., 22, 81-86, (1975) · Zbl 0314.47031
[4] Schu, J., Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. austral. math. soc., 43, 153-159, (1991) · Zbl 0709.47051
[5] Tan, K.K.; Xu, H.K., Fixed point iteration processes for asymptotically nonexpansive mappings, Proc. amer. math. soc., 122, 733-739, (1994) · Zbl 0820.47071
[6] Agarwal, R.P.; Qin, X.; Kang, S.M., Strong convergence theorems for strongly continuous semigroups of pseudocontractions, Appl. math. lett., 24, 1845-1848, (2011) · Zbl 1242.47045
[7] Qin, X.; Cho, Y.J.; Kang, S.M.; Zhou, H., Convergence theorems of common fixed points for a family of Lipschitz quasi-pseudocontractions, Nonlinear anal., 71, 685-690, (2009) · Zbl 1168.47304
[8] Qin, X.; Cho, Y.J.; Zhou, H., Strong convergence theorems of fixed point for quasi-pseudo-contractions by hybrid projection algorithms, Fixed point theory, 11, 347-354, (2010) · Zbl 1250.47074
[9] Qin, X.; Zhou, H.; Kang, S.M., Strong convergence of Mann type implicit iterative process for demi-continuous pseudo-contractions, J. appl. math. comput., 29, 217-228, (2009) · Zbl 1222.47110
[10] Yao, Y.; Liou, Y.C.; Marino, G., A hybrid algorithm for pseudo-contractive mappings, Nonlinear anal., 71, 4997-5002, (2009) · Zbl 1222.47128
[11] Zhou, H., Strong convergence theorems for a family of Lipschitz quasi-pseudo-contractions in Hilbert spaces, Nonlinear anal., 71, 120-125, (2009) · Zbl 1225.47123
[12] Y. Haugazeau, Sur les inéquations variationnelles et la minimisation de fonctionnelles convexes, Ph.D. Thesis, Université de Paris 1968.
[13] Zhou, H., Convergence theorems of fixed points for Lipschitz pseudo-contractions in Hilbert spaces, J. math. anal. appl., 343, 546-556, (2008) · Zbl 1140.47058
[14] Lan, K.Q.; Wu, J.H., Convergence of approximants for demicontinuous pseudo-contractive maps in Hilbert spaces, Nonlinear anal., 49, 737-746, (2002) · Zbl 1019.47040
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