References
- Ya. I. Alber, Metric and generalized projection operators in Banach spaces: properties and applications, in: A. G. Kartsatos (Ed.), Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, Marcel Dekker, New York, 1996, pp. 15-50.
- Ya. I. Alber and S. Reich, An iterative method for solving a class of nonlinear operator equations in Banach spaces, Panamer. Math. J., 4(1994), 39-54.
- D. Butnariu, S. Reich and A. J. Zaslavski, Asymptotic behavior of relatively nonexpansive operators in Banach spaces, J. Appl. Anal., 7(2001), 151-174. https://doi.org/10.1515/JAA.2001.151
- D. Butnariu, S. Reich and A. J. Zaslavski, Weak convergence of orbits of nonlinear operators in reflexive Banach spaces, Numer. Funct. Anal. Optim., 24(2003), 489-508. https://doi.org/10.1081/NFA-120023869
- Y. Censor and S. Reich, Iterations of paracontractions and firmly nonexpansive operators with applications to feasibility and optimization, Optimization, 37(1996), 323-339. https://doi.org/10.1080/02331939608844225
- C. E. Chidume and S. A. Mutangadura, An example on the Mann iteration method for Lipschitz pseudocontractions, Proc. Amer. Math. Soc., 129(2001), 2359-2363. https://doi.org/10.1090/S0002-9939-01-06009-9
- I. Cioranescu, Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems, Kluwer Academic Publishers, Dordrecht, 1990.
- A. Genel and J. Lindenstrass, An example concerning fixed points, Israel J. Math., 22(1975), 81-86. https://doi.org/10.1007/BF02757276
- K. Goebel and W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 35(1972), 171-174. https://doi.org/10.1090/S0002-9939-1972-0298500-3
- B. Halpern, Fixed points of nonexpanding maps, Bull. Amer. Math. Soc., 73(1967), 957-961. https://doi.org/10.1090/S0002-9904-1967-11864-0
- S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc., 44(1974), 147-150. https://doi.org/10.1090/S0002-9939-1974-0336469-5
- S. Kamimura and W. Takahashi, Strong convergence of a proxiaml-type algorithm in a Banach space, SIAM J. Optim., 13(2003), 938-945.
- T. H. Kim and H. K. Xu, Strong convergence of modified Mann iterations, Nonlinear Anal., 61(2005), 51-60. https://doi.org/10.1016/j.na.2004.11.011
- T. H. Kim and H. K. Xu, Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Anal., 64(2006), 1140- 1152. https://doi.org/10.1016/j.na.2005.05.059
- P. L. Lions, Approximation de points fixes de contractions, C. R. Acad. Sci. S`er. A-B Paris, 284(1977), 1357-1359.
- W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc., 4(1953), 506-510. https://doi.org/10.1090/S0002-9939-1953-0054846-3
- C. Martinez-Yanes and H. K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal., 64(2006), 2400-2411. https://doi.org/10.1016/j.na.2005.08.018
- S. Matsushita and W. Takahashi, A strong convergence theorem for relatively nonexpansive mappings in a Banach space, J. Approx. Theory, 134(2005), 257-266. https://doi.org/10.1016/j.jat.2005.02.007
- K. Nakajo and W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl., 279(2003), 372-379. https://doi.org/10.1016/S0022-247X(02)00458-4
- S. Reich, Strong convergence theorems for resolvents of accretive operators in Banach spaces, J. Math. Anal. Appl., 75(1980), 287-292. https://doi.org/10.1016/0022-247X(80)90323-6
- S. Reich, Weak convergence theorems for nonexpansive mappings in Banach spaces, J. Math. Anal. Appl., 67(1979), 274-276. https://doi.org/10.1016/0022-247X(79)90024-6
- S. Reich, Review of Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems, Kluwer Academic Publishers, Dordrecht, 1990, Bull. Amer. Math. Soc., 26(1992), 367-370. https://doi.org/10.1090/S0273-0979-1992-00287-2
- S. Reich, A weak convergence theorem for the alternating method with Bregman distance, in:A. G. Kartsatos (Ed.), Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, Marcel Dekker, New York, 1996, pp. 313-318.
- N. Shioji and W. Takahashi, Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces, Proc. Amer. Math. Soc., 125(1997), 3641-3645. https://doi.org/10.1090/S0002-9939-97-04033-1
- W. Takahashi, Nonlinear Functional Analysis, Yokohama Publishers, Yokohama, 2000.
- R. Wittmann, Approximation of fixed points of nonexpansive mappings, Arch. Math., 58(1992), 486-491. https://doi.org/10.1007/BF01190119
- H. K. Xu, Existence and convergence for fixed points of mappings of asymptotically nonexpansive type, Nonlinear Anal., 16(1991), 1139-1146. https://doi.org/10.1016/0362-546X(91)90201-B
- H. K. Xu, Inequalities in Banach spaces with applications, Nonlinear Anal., 16(1991), 1127-1138. https://doi.org/10.1016/0362-546X(91)90200-K
- H. K. Xu, Iterative algorithms for nonlinear operators, J. London Math. Soc., 66(2002), 240-256. https://doi.org/10.1112/S0024610702003332
Cited by
- Parallel Hybrid Iterative Methods for Variational Inequalities, Equilibrium Problems, and Common Fixed Point Problems vol.44, pp.2, 2016, https://doi.org/10.1007/s10013-015-0129-z
- Convergence theorems based on the shrinking projection method for variational inequality and equilibrium problems vol.37, pp.1-2, 2011, https://doi.org/10.1007/s12190-010-0427-2
- Strong Convergence of Modified Iteration Processes for Relatively Weak Nonexpansive Mappings vol.52, pp.4, 2012, https://doi.org/10.5666/KMJ.2012.52.4.433