Some results on zero points of m-accretive operators in reflexive Banach spaces
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Bruck RE: Nonexpansive projections on subsets of Banach spaces. Pac. J. Math. 1973, 47: 341–355. 10.2140/pjm.1973.47.341
Reich S: Asymptotic behavior of contractions in Banach spaces. J. Math. Anal. Appl. 1973, 44: 57–70. 10.1016/0022-247X(73)90024-3
Goebel K, Reich S: Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings. Dekker, New York; 1984.
Bauschke HH, Matousková E, Reich S: Projection and proximal point methods: convergence results and counterexamples. Nonlinear Anal. 2004, 56: 715–738. 10.1016/j.na.2003.10.010
Reich S: Weak convergence theorems for nonexpansive mappings in Banach spaces. J. Math. Anal. Appl. 1979, 67: 274–276. 10.1016/0022-247X(79)90024-6
Genel A, Lindenstruss J: An example concerning fixed points. Isr. J. Math. 1975, 22: 81–86. 10.1007/BF02757276
Cho SY, Li W, Kang SM: Convergence analysis of an iterative algorithm for monotone operators. J. Inequal. Appl. 2013., 2013: Article ID 199
Cho SY, Qin X: On the strong convergence of an iterative process for asymptotically strict pseudocontractions and equilibrium problems. Appl. Math. Comput. 2014, 235: 430–438.
Yang S, Zhang MY: Strong convergence theorems for fixed points of generalized asymptotically quasi- ϕ -nonexpansive mappings. Adv. Fixed Point Theory 2014, 4: 69–90.
Cho SY, Qin X, Kang SM: Hybrid projection algorithms for treating common fixed points of a family of demicontinuous pseudocontractions. Appl. Math. Lett. 2012, 25: 854–857. 10.1016/j.aml.2011.10.031
Zhou H: Convergence theorems of common fixed points for a family of Lipschitz quasi-pseudocontractions. Nonlinear Anal. 2009, 71: 685–690. 10.1016/j.na.2008.10.102
Qin X, Agarwal RP: Shrinking projection methods for a pair of asymptotically quasi- ϕ -nonexpansive mappings. Numer. Funct. Anal. Optim. 2010, 31: 1072–1089. 10.1080/01630563.2010.501643
Chen JH: Iterations for equilibrium and fixed point problems. J. Nonlinear Funct. Anal. 2013., 2013: Article ID 4
Hao Y: Some results on a modified Mann iterative scheme in a reflexive Banach space. Fixed Point Theory Appl. 2013., 2013: Article ID 227
Kim JK: Strong convergence theorems by hybrid projection methods for equilibrium problems and fixed point problems of the asymptotically quasi- ϕ -nonexpansive mappings. Fixed Point Theory Appl. 2011., 2011: Article ID 10
Qin X, Cho SY, Kang SM: Strong convergence of shrinking projection methods for quasi- ϕ -nonexpansive mappings and equilibrium problems. J. Comput. Appl. Math. 2010, 234: 750–760. 10.1016/j.cam.2010.01.015
Wu C, Sun L: A monotone projection algorithm for fixed points of nonlinear operators. Fixed Point Theory Appl. 2013., 2013: Article ID 318
Wu C, Lv S: Bregman projection methods for zeros of monotone operators. J. Fixed Point Theory 2013., 2013: Article ID 7
Qin X, Su Y: Strong convergence theorems for relatively nonexpansive mappings in a Banach space. Nonlinear Anal. 2007, 67: 1958–1965. 10.1016/j.na.2006.08.021
Ye J, Huang J: Strong convergence theorems for fixed point problems and generalized equilibrium problems of three relatively quasi-nonexpansive mappings in Banach spaces. J. Math. Comput. Sci. 2011, 1: 1–18. 10.9734/BJMCS/2011/120
Qin X, Cho YJ, Kang SM: Convergence theorems of common elements for equilibrium problems and fixed point problems in Banach spaces. J. Comput. Appl. Math. 2009, 225: 20–30. 10.1016/j.cam.2008.06.011
Halpern B: Fixed points of nonexpanding maps. Bull. Am. Math. Soc. 1967, 73: 957–961. 10.1090/S0002-9904-1967-11864-0
Qin X, Cho SY, Wang L: A regularization method for treating zero points of the sum of two monotone operators. Fixed Point Theory Appl. 2014., 2014: Article ID 75
Takahashi W: Viscosity approximation methods for resolvents of accretive operators in Banach spaces. J. Fixed Point Theory Appl. 2007, 1: 135–147. 10.1007/s11784-006-0004-3
Song J, Chen M: A modified Mann iteration for zero points of accretive operators. Fixed Point Theory Appl. 2013., 2013: Article ID 347
Qin X, Su Y: Approximation of a zero point of accretive operator in Banach spaces. J. Math. Anal. Appl. 2007, 329: 415–424. 10.1016/j.jmaa.2006.06.067
Yang S: Zero theorems of accretive operators in reflexive Banach spaces. J. Nonlinear Funct. Anal. 2013., 2013: Article ID 2
Qing Y, Cho SY: A regularization algorithm for zero points of accretive operators. Fixed Point Theory Appl. 2013., 2013: Article ID 341
Qing Y, Cho SY: Proximal point algorithms for zero points of nonlinear operators. Fixed Point Theory Appl. 2014., 2014: Article ID 42
Reich S: Strong convergence theorems for resolvents of accretive operators in Banach spaces. J. Math. Anal. Appl. 1980, 75: 287–292. 10.1016/0022-247X(80)90323-6
Liu LS: Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces. J. Math. Anal. Appl. 1995, 194: 114–125. 10.1006/jmaa.1995.1289
Bruck RE: Properties of fixed-point sets of nonexpansive mappings in Banach spaces. Trans. Am. Math. Soc. 1973, 179: 251–262.
Chang SS: Some problems and results in the study of nonlinear analysis. Nonlinear Anal. 1997, 30: 4197–4208. 10.1016/S0362-546X(97)00388-X
Qin X, Cho SY, Wang L: Iterative algorithms with errors for zero points of m -accretive operators. Fixed Point Theory Appl. 2013., 2013: Article ID 148