References
- R. P. Agarwal, D. O'Regan, and D. R. Sahu, Fixed Point Theory for Lipschitzian-type Mappings with Applications, Springer, 2009.
- V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Space, Noordhoff, Leyden, 1976.
- H. H. Bauschke, P. L. Combettes, and S. Reich, The asymptotic behavior of the composition of two resolvents, Nonlinear Anal. 60 (2005), no. 2, 283-301. https://doi.org/10.1016/j.na.2004.07.054
- H. H. Bauschke, E. Matouskova and S. Reich, Projection and proximal point methods convergence results and counterexamples, Nonlinear Anal. 56 (2004), no. 5, 715-738. https://doi.org/10.1016/j.na.2003.10.010
- L. M. Bregman, The method of successive projection for finding a common point of convex sets, Sov. Math. Dokl. 6 (1965), 688-692.
- I. Cioranescu, Geometry of Banach Spaces, "Duality Mappings and Nonlinear Problems", Kluwer Academic Publishers, Dordrecht, 1990.
- K. Goebel and W. A. Kirk, Topics in Metric Fixed Point Theory, Cambridge Stud. Adv. Math. 28, Cambridge Univ. Press, Cambridge, UK, 1990.
- K. Goebel and S. Reich, Uniform Convexity, Hyperbolic Geometry and Nonexpansive Mappings, Marcel Dekker, New York and Basel, 1984.
- A. A. Goldstein, Convex programming in Hilbert space, Bull. Amer. Math. Soc. 70 (1964), 709-710. https://doi.org/10.1090/S0002-9904-1964-11178-2
- G. Guler, On the convergence of the proximal point algorithm for convex minimization, SIAM J. Control Optim. 29 (1991), no. 2, 403-419. https://doi.org/10.1137/0329022
- H. Hundal, An alternating projection that does not converge in norm, Nonlinear Anal. 57 (2004), no. 1, 35-61. https://doi.org/10.1016/j.na.2003.11.004
- J. S. Jung, Viscosity approximation methods for a family of finite nonexpansive mappings in Banach spaces, Nonlinear Anal. Appl. 64 (2006), no. 11, 2536-2552. https://doi.org/10.1016/j.na.2005.08.032
- J. S. Jung, Iterative methods for pseudocontractive mappings in Banach spaces, Abstr. Appl. Anal. 2013 (2013), Article ID 643602, 7 pages.
- J. K. Kim and N. Buong, Convergence rates in regularization for a system of nonlinear ill-posed equations with m-accretive operators, J. Inequal. Appl. 2014 (2014), no. 440, 9 pages.
- J. K. Kim and T. M. Tuyen, Regularization proximal point algorithm for finding a common fixed point of a finite family of nonexpansive mappings in Banach spaces, Fixed Point Theory Appl. 2011 (2011), no. 52, 10 pages.
- N. Lehdili and A. Moudafi, Combining the proximal algorithm and Tikhonov regularization, Optim. 37 (1996), no. 3, 239-252. https://doi.org/10.1080/02331939608844217
- E. S. Levitin and B. T. Polyak, Constrained Minimization Method, USSR Comput. Math. Math. Phys. 6 (1966), 1-50.
- B. Martinet, Regularisation d'inequations variationnelles par approximations successives, (French) Rev. Francaise Informat. Recherche Operationnalle 4 (1970), Ser. R-3, 154-158.
- J. von Neumann, Functional Operators. II. The Geometry of Orthogonal Space, Annals of Mathematics Studies, no. 22. Princeton University Press, Princeton, N. J., 1950.
- Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 591-597. https://doi.org/10.1090/S0002-9904-1967-11761-0
- W. V. Petryshn, A characterization of strict convexity of Banach spaces and other uses of duality mappings, J. Funct. Anal. 6 (1970), 282-291. https://doi.org/10.1016/0022-1236(70)90061-3
- R. T. Rockafellar, Characterization of the subdifferentials of convex functions, Pacific J. Math. 17 (1966), 497-510. https://doi.org/10.2140/pjm.1966.17.497
- R. T. Rockafellar, On the maximality of sums of nonlinear monotone operators, Trans. Amer. Math. Soc. 149 (1970), 75-88. https://doi.org/10.1090/S0002-9947-1970-0282272-5
- R. T. Rockafellar, Monotone operators and proximal point algorithm, SIAM J. Control Optim. 14 (1976), no. 5, 877-898. https://doi.org/10.1137/0314056
- D. R. Sahu and J. C. Yao, The prox-Tikhonov regularization method for the proximal point algorithm in Banach spaces, J. Global Optim. 51 (2011), no. 4, 641-655. https://doi.org/10.1007/s10898-011-9647-8
- Y. Song and C. Yang, A note on a paper: A regularization method for the proximal point algorithm, J. Global Optim. 43 (2009), no. 1, 171-174. https://doi.org/10.1007/s10898-008-9279-9
- S. Takahashi, W. Takahashi, and M. Toyoda, Strong convergence theorems for maximal monotone operators with nonlinear mappings in Hilbert spaces, J. Optim. Theory Appl. 147 (2010), no. 1, 27-41. https://doi.org/10.1007/s10957-010-9713-2
- T. M. Tuyen, A regularization proximal point algorithm for zeros of accretive operators in Banach spaces, Afr. Diaspora J. Math. 13 (2012), no. 2, 62-73.
- T. M. Tuyen, Strong convergence theorem for a common zero of maccretive mappings in Banach spaces by viscosity approximation methods, Nonl. Func. Anal. Appl. 17 (2012), no. 2, 187-197.
- N. C. Wong, D. R. Sahu, and J. C. Yao, Solving variational inequalities involving nonexpansive type mappings, Nonlinear Anal. 69 (2008), no. 12, 4732-4753. https://doi.org/10.1016/j.na.2007.11.025
- H. K. Xu, A regularization method for the proximal point algorithm, J. Global Optim. 36 (2006), no. 1, 115-125. https://doi.org/10.1007/s10898-006-9002-7
- H. K. Xu, Strong convergence of an iterative method for nonexpansive and accretive operators, J. Math. Anal. Appl. 314 (2006), no. 2, 631-643. https://doi.org/10.1016/j.jmaa.2005.04.082