A new hybrid algorithm for a nonexpansive mapping
Tóm tắt
In the paper, we introduce a new hybrid algorithm which is not based on the modification to weak convergence algorithms. The strong convergence theorem of the proposed algorithm is presented. Finally, the numerical experiments suggest that the new algorithm could be faster than Nakajo and Takahashi’s algorithm in J. Math. Anal. Appl. 279:372-379, 2003.
Tài liệu tham khảo
Xu, HK: A variable Krasnosel’skiĭ-Mann algorithm and the multiple-set split feasibility problem. Inverse Probl. 22, 2021-2034 (2006)
Combettes, PL: On the numerical robustness of the parallel projection method in signal synthesis. IEEE Signal Process. Lett. 8(2), 45-47 (2001)
Podilchuk, CI, Mammone, RJ: Image recovery by convex projections using a least-squares constraint. J. Opt. Soc. Am. 7(3), 517-521 (1990)
Youla, D: Mathematical theory of image restoration by the method of convex projection. In: Stark, H (ed.) Image Recovery Theory and Applications, pp. 29-77. Academic Press, Orlando (1987)
Halpern, B: Fixed points of nonexpanding maps. Bull. Am. Math. Soc. 73, 957-961 (1967)
Moudafi, A: Viscosity approximation methods for fixed-points problems. J. Math. Anal. Appl. 241, 46-55 (2000)
Xu, HK: Viscosity approximation methods for nonexpansive mappings. J. Math. Anal. Appl. 298, 279-291 (2004)
Mann, WR: Mean value methods in iteration. Proc. Am. Math. Soc. 4, 506-510 (1953)
Genel, A, Lindenstrass, J: An example concerning fixed points. Isr. J. Math. 22, 81-86 (1975)
Bauschke, HH, Combettes, PL: A weak-to-strong convergence principle for Fejér-monotone methods in Hilbert spaces. Math. Oper. Res. 26(2), 248-264 (2001)
Nakajo, K, Takahashi, W: Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups. J. Math. Anal. Appl. 279, 372-379 (2003)
Kim, TH, Xu, HK: Strong convergence of modified Mann iterations. Nonlinear Anal. 61, 51-60 (2005)
Marino, G, Xu, HK: Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces. J. Math. Anal. Appl. 329, 336-346 (2007)
Yao, Y, Liou, YC, Marino, G: A hybrid algorithm for pseudo-contractive mappings. Nonlinear Anal. 71, 4997-5002 (2009)
Zeng, LC, Ansari, QH, Al-Homidan, S: Hybrid proximal-type algorithms for generalized equilibrium problems, maximal monotone operators and relatively nonexpansive mappings. Fixed Point Theory Appl. 2011, Article ID 973028 (2011)
Ceng, LC, Ansari, QH, Yao, JC: Hybrid proximal-type and hybrid shrinking projection algorithms for equilibrium problems, maximal monotone operators and relatively nonexpansive mappings. Numer. Funct. Anal. Optim. 31(7), 763-797 (2010)
Ceng, LC, Guu, SM, Yao, JC: Hybrid viscosity CQ method for finding a common solution of a variational inequality, a general system of variational inequalities, and a fixed point problem. Fixed Point Theory Appl. 2013, Article ID 313 (2013)
Zhou, H, Su, Y: Strong convergence theorems for a family of quasi-asymptotic pseudo-contractions in Hilbert spaces. Nonlinear Anal. 70, 4047-4052 (2009)
Nilsrakoo, W, Saejung, S: Weak and strong convergence theorems for countable Lipschitzian mappings and its applications. Nonlinear Anal. 69, 2695-2708 (2008)
Malitsky, YV, Semenov, VV: A hybrid method without extrapolation step for solving variational inequality problems. J. Glob. Optim. 61(1), 193-202 (2015)
Goebel, K, Kirk, WA: Topics in Metric Fixed Point Theory. Cambridge Studies in Advanced Mathematics, vol. 28. Cambridge University Press, Cambridge (1990)
Matinez-Yanes, C, Xu, HK: Strong convergence of the CQ method for fixed point processes. Nonlinear Anal. 64, 2400-2411 (2006)
He, S, Yang, C, Duan, P: Realization of the hybrid method for Mann iterations. Appl. Math. Comput. 217, 4239-4247 (2010)