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Approximation methods for common fixed points of nonexpansive mappings in Hilbert spaces. (English) Zbl 1111.47058
The author studies implicit and explicit viscosity-like methods for finding specific fixed points of infinite countable families of nonexpansive self-mappings in Hilbert spaces. He obtains strong convergence results. His results are of practical interest from the numerical point of view.

MSC:
47J25Iterative procedures (nonlinear operator equations)
47H09Mappings defined by “shrinking” properties
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
65J15Equations with nonlinear operators (numerical methods)
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References:
[1] Bauschke, H. H.: The approximation of fixed points of compositions of nonexpansive mappings in Hilbert space. J. math. Anal. appl. 202, No. 1, 150-159 (1996) · Zbl 0956.47024
[2] Browder, F. E.: Convergence of approximants to fixed points of non-expansive maps in Banach spaces. Arch. ration. Mech. anal. 24, 82-90 (1967) · Zbl 0148.13601
[3] Combettes, P. L.: Construction d’un point fixe commun d’une famille de contractions fermes. C. R. Acad. sci. Paris sér. Math. 320, No. 11, 1385-1390 (1995) · Zbl 0830.65047
[4] Ciric, L. J. B.; Ume, J. S.; Khan, M. S.: On the convergence of the Ishikawa iterates to a common fixed point of two mappings. Arch. math. (Brno) 39, 123-127 (2003) · Zbl 1109.47312
[5] Goebel, K.; Kirk, W. A.: Topics in metric fixed point theory. Cambridge stud. Adv. math. 28 (1990) · Zbl 0708.47031
[6] Halpern, B.: Fixed points of nonexpanding maps. Bull. amer. Math. soc. 73, 957-961 (1967) · Zbl 0177.19101
[7] Kimura, Y.; Takahashi, W.; Toyoda, M.: Convergence to common fixed points of a finite family of nonexpansive mappings. Arch. math. 84, No. 4, 350-363 (2005) · Zbl 1086.47051
[8] Lions, P. L.: Approximation de points fixes de contractions. C. R. Acad. sci. Paris sér. A 284, 1357-1359 (1977) · Zbl 0349.47046
[9] Moudafi, A.: Viscosity approximations methods for fixed-points problems. J. math. Anal. appl. 241, 46-55 (2000) · Zbl 0957.47039
[10] O’hara, J. G.; Pillay, P.; Xu, H. K.: Iterative approaches to finding nearest common fixed points of nonexpansive mappings in Hilbert spaces. Nonlinear anal. 54, 1417-1426 (2003) · Zbl 1052.47049
[11] Sun, Z. H.: Strong convergence of a implicit iterative process for a finite family of asymptotically quasi-nonexpansive mappings. J. math. Anal. appl. 286, 351-358 (2003) · Zbl 1095.47046
[12] Wittman, R.: Approximation of fixed points of nonexpansive mappings. Arch. math. 58, 486-491 (1992) · Zbl 0797.47036
[13] Xu, H. K.; Ori, M. G.: An implicit iterative process for nonexpansive mappings. Numer. funct. Anal. optim. 22, 767-773 (2001) · Zbl 0999.47043
[14] Yamada, I.; Ogura, N.: Hybrid steepest descent method for the variational inequality problem over the fixed point set of certain quasi-nonexpansive mappings. Numer. funct. Anal. optim. 25, No. 7 -- 8, 619-655 (2004) · Zbl 1095.47049
[15] Zhou, Y. Y.; Chang, S. S.: Convergence of implicit iterative process for a finite family of asymptotically nonexpansive mappings in Banach spaces. Numer. funct. Anal. optim. 23, 911-921 (2002) · Zbl 1041.47048