References
- [1] Y. Censor, T. Elfving, A multiprojection algorithms using Bragman projection in a product space, Numer. Algorithm, 8 (1994), 221–239.
- [2] C. Byrne, A unified treatment of some iterative algorithms in signal processing and image reconstruction, Inverse Problem, 20 (2004), 103–120.
- [3] Y. Censor, T. Bortfeld, B. Martin, A. Trofimov, A unified approach for inversion problems in intensity-modulated radiation therapy, Phys. Med. Biol., 51 (2006), 2353–2365.
- [4] Y. Censor, W. Chen, P. L. Combettes, R. Davidi, G. T. Herman, On the effectiveness of the projection methods for convex feasibility problems with linear inequality constraints, Comput. Optim. Appl., 17 (2011), 1–24.
- [5] Y. Censor, A. Segal, The split common fixed point problem for directed operators, J. Convex Anal., 16 (2009), 587–600.
- [6] Y. Censor, A. Gibali, S. Reich, Algorithms for the split variational in-equality problem, Numerical Algorithms, 59 (2012), 301–323.
- [7] C. Byrne, Y. Censor, A. Gibali, S. Reich, The split common null point problem, J. Nonlinear Convex Anal., 13 (2012), 759–775.
- [8] S. S. Chang, R. P. Agarwal, Strong convergence theorems of general split equality problems for quasi-nonexpansive mappings, J. Inequal. Appl., (2014), 2014:367.
- [9] R. Kraikaew, S. Saejung, On split common fixed point problems, J. Math. Anal. Appl., 415 (2014), 513–524.
- [10] M. Eslamian, J. Vahidi, Split Common Fixed Point Problem of Nonexpansive Semigroup, Mediterr. J. Math., 13 (2016), 1177–1195.
- [11] W. Takahashi, H. K. Xu, J. C. Yao, Iterative Methods for Generalized Split Feasibility Problems in Hilbert Spaces, Set-Valued and Variational Analysis., 23 (2015), 205–221.
- [12] Y. Shehu, F. U. Ogbuisi, O. S. Iyiola, Convergence Analysis of an iterative algorithm for fixed point problems and split feasibility problems in certain Banach spaces, Optimization, 2015. doi:10.1080/02331934.2015.1039533
- [13] M. Eslamian, General algorithms for split common fixed point problem of demicontractive mappings, Optimization, 65 (2016), 443–465.
- [14] P. L. Lions, B. Mercier, Splitting algorithms for the sum of two nonlinear operators, SIAM J. Numer. Anal., 16 (1979), 964–979.
- [15] G. B. Passty, Ergodic convergence to a zero of the sum of monotone operators in Hilbert space, J. Math. Anal. Appl.72 (1979), 383–390.
- [16] S. P. Han, G. Lou, A parallel algorithm for a class of convex programs, SIAM J. Control Optim.26 (1988), 345–355.
- [17] J. Eckstein, B. F. Svaiter, A family of projective splitting methods for the sum of two maximal monotone operators, Math. Program, 111 (2008), 173–199.
- [18] A. Moudafi, Split Monotone Variational Inclusions, J. Optim. Theory Appl.150 (2011), 275–283.
- [19] A. Moudafi, A relaxed alternating CQ algorithm for convex feasibility problems, Nonlinear Analysis, 79 (2013), 117–121.
- [20] H. Attouch, A. Cabot, F. Frankel, J. Peypouquet, Alternating proximal algorithms for constrained variational inequalities. Application to domain decomposition for PDEs, Nonlinear Anal.74 (2011), 7455–7473.
- [21] H. Attouch, J. Bolte, P. Redont, A. Soubeyran, Alternating proximal algorithms for weakly coupled minimization problems. Applications to dynamical games and PDEs, J. Convex Anal.15 (2008), 485–506.
- [22] A. Moudafi, Alternating CQ-algorithm for convex feasibility and split fixed-point problems, J. Nonlinear Convex Anal., 15 (2014), 809–818.
- [23] J. Zhao, Solving split equality fixed-point problem of quasi-nonexpansive mappings without prior knowledge of operators norms, Optimization, (2014), doi(10.1080/02331934.2014.883515).
- [24] S. Takahashi, W. Takahashi, M. Toyoda, Strong convergence theorems for maximal monotone operators with nonlinear mappings in Hilbert spaces, J. Optim. Theory Appl., 147 (2010), 27–41.
- [25] N. Shahzad, H. Zegeye, Approximating a common point of fixed points of a pseudocontractive mapping and zeros of sum of monotone mappings, Fixed Point Theory and Applications, 2014, 2014:85.
- [26] P. E. Mainge, A hybrid extragradient-viscosity method for monotone operators and fixed point problems, SIAM J. Control Optim.47 (2008), 1499–1515.
- [27] H. Iiduka, I. Yamada, A use of conjugate gradient direction for the convex optimization problem over the fixed point set of a nonexpansive mapping, SIAM J. Optim.19 (2009), 1881–1893.
- [28] A. Latif, M. Eslamian, Strong convergence and split common fixed point problem for set-valued operators, J. Nonlinear Convex Anal.17 (2016), 967–986.
- [29] A. Abkar, M. Eslamian, Convergence theorems for a finite family of generalized nonexpansive multivalued mappings in CAT(0) spaces, Nonlinear Analysis, 75 (2012), 1895–1903.
- [30] A. Abkar, M. Eslamian, Geodesic metric spaces and generalized nonexpansive multivalued mappings, Bull. Iran. Math. Soc., 39 (2013), 993–1008.
- [31] R. T. Rockafellar, On the maximal monotonicity of subdifferential mappings, Pac. J. Math., 33 (1970), 209–216.
- [32] W. Takahashi, Introduction to Nonlinear and Convex Analysis. Yokohama Publishers, Yokohama (2009).
- [33] H. Zegeye, N. Shahzad, Convergence of Mann’s type iteration method for generalized asymptotically nonexpansive mappings, Comput. Math. Appl., 62 (2011), 4007–4014.
- [34] H. K. Xu, Iterative algorithms for nonlinear operators, J. Lond. Math. Soc., 66 (2002), 240–256.
- [35] P. E. Mainge, Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization, Set-Valued Analysis, 16 (2008), 899–912.
- [36] E. Blum, W. Oettli, From optimization and variational inequalities to equilibrium problems, Math. Student, 63 (1994), 123–145.
- [37] P. L. Combettes, S. A. Hirstoaga, Equilibrium programming in Hilbert spaces, J. Nonlinear Convex Anal., 6 (2005), 117–136.
- [38] S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl., 331 (2007), 506–515.
- [39] V. Colao, G. Marino, L. Muglia, Viscosity methods for common solutions for equilibrium and hierarchical fixed point problems, Optimization, 60 (2011), 553–573.
- [40] M. Eslamian, Hybrid method for equilibrium problems and fixed point problems of finite families of nonexpansive semigroups, Rev. R. Acad. Cienc. Exactas Fs. Nat., Ser. A Mat., 107 (2013), 299–307.
- [41] L. C. Ceng, A. Petrusel, J. C. Yao, Composite viscosity approximation methods for equilibrium problem, variational inequality and common fixed points. J. Nonlinear Convex Anal., 15 (2014), 219–240.
- [42] P. T. Vuong, J. J. Strodiot, V. H. Hien Nguyen, On extragradient-viscosity methods for solving equilibrium and fixed point problems in a Hilbert space, Optimization, 64 (2015), 429–451.