An inertial self-adaptive algorithm for the generalized split common null point problem in Hilbert spaces

Agarwal, R.P., O’Regan, D., Sahu, D.R.: Fixed Point Theory for Lipschitzian Type Mappings with Applications. Springer, Berlin (2009)

Alber, Y.I., Iusem, A.N.: Extension of subgradient techniques for nonsmooth optimization in Banach spaces. Set-Valued Anal. 9, 315–335 (2001)

Alvarez, F.: Weak convergence of a relaxed and inertial hybrid projectionproximal point algorithm for maximal monotone operators in Hilbert space. SIAM J. Optim. 14, 773–782 (2004)

Alvarez, F., Attouch, H.: An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping. Set-Valued Anal. 9, 3–11 (2001)

Bruck, R.E., Reich, S.: Nonexpansive projections and resolvents of accretive operators in Banach spaces. Houston J. Math. 3, 459–470 (1977)

Byrne, C.: Iterative oblique projection onto convex sets and the split feasibility problem. Inverse Probl. 18, 441–453 (2002)

Byrne, C.: A unified treatment of some iterative algorithms in signal processing and image reconstruction. Inverse Probl. 20, 103–120 (2004)

Byrne, C., Censor, Y., Gibali, A., Reich, S.: The split common null point problem. J. Nonlinear Convex Anal. 13, 759–775 (2012)

Censor, Y., Elfving, T.: A multiprojection algorithm using Bregman projections in product space. Numer. Algorithms 8, 221–239 (1994)

Chen, C., Ma, S., Yang, J.: A general inertial proximal point algorithm for mixed variational inequality problem. SIAM J. Optim. 25, 2120–2142 (2015)

Cholamjiak, W., Cholamjiak, P., Suantai, S.: An inertial forward-backward splitting method for solving inclusion problems in Hilbert spaces. J. Fixed Point Theory Appl. 20, 42 (2018)

Combettes, P.L., Hirstoaga, A.: Equilibrium programming in Hilbert spaces. J. Nonlinear Convex Anal. 6, 117–136 (2005)

Combettes, P.L., Pesquet, J.C.: Proximal splitting methods in signal processing. Fixed Point Algorithms Inverse Probl. Sci. Eng. 49, 185–212 (2011)

Deimling, K.: Nonlinear Functional Analysis. Springer, Berlin (1985)

Dong, Q.L., Heab, S., Zhaoab, J.: Solving the split equality problem without prior knowledge of operator norms. Optimization 64(9), 1887–1906 (2015)

Gobel, K.A., Kirk, W.A.: Topics in Metric Fixed Point Theory, Cambridge Studied in Advanced Mathematics, vol. 28. Cambridge University Press, Cambridge (1990)

Goebel, K., Reich, S.: Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings. Marcel Dekker, New York (1984)

Hendrickx, J.M., Olshevsky, A.: Matrix $$p$$-norms are NP-hard to approximate if $$P= 1, 2,\infty $$. SIAM. J. Matrix Anal. Appl. 31, 2802–2812 (2010)

He, S., Yang, C.: Solving the variational inequality problem defined on intersection of finite level sets. Abstract Appl. Anal. 2013, 8 (2013)

Kesornprom, S., Pholasa, N., Cholamjiak, P.: On the convergence analysis of the gradient-CQ algorithms for the split feasibility problem. Numer. Algorithms 84, 997–1017 (2020)

Khan, S.A., Suantai, S., Cholamjiak, W.: Shrinking projection methods involving inertial forward-backward splitting methods for inclusion problems. RACSAM 113, 645–656 (2019)

López, G., Martin-Marquez, V., Wang, F., Xu, H.-K.: Solving the split feasibility problem without prior knowledge of matrix norms. Inverse Probl. 28, 085004 (2012)

Masad, E., Reich, S.: A note on the multiple-set split convex feasibility problem in Hilbert space. J. Nonlinear Convex Anal. 3, 357–371 (2007)

Maingé, P.E.: Approximation methods for common fixed points of nonexpansive mappings in Hilbert spaces. J. Math. Anal. Appl. 325, 469–479 (2007)

Maingé, P.E.: Regularized and inertial algorithms for common fixed points of nonlinear operators. J. Math. Anal. Appl. 34, 876–887 (2008)

Marino, G., Xu, H.K.: Convergence of generalized proximal point algorithms. Commun. Pure Appl. Anal. 3(4), 791–808 (2004)

Moudafi, A., Elisabeth, E.: An approximate inertial proximal method using enlargement of a maximal monotone operato. Int. J. Pure Appl. Math. 5, 283–299 (2003)

Moudafi, A., Thakur, B.S.: Solving proximal split feasibility problems without prior knowledge of operator norms. Optim. Lett. 8, 2099–2110 (2014)

Ogbuisi, F.U., Mewomo, O.T.: On split generalised mixed equilibrium problems and fixed-point problems with no prior knowledge of operator norm. J. Fixed Point Theory Appl. 19, 2109–2128 (2017)

Polyak, B.T.: Some methods of speeding up the convergence of iteration methods. USSR Comput. Math. Math. Phys. 4, 1–17 (1964)

Pascali, D., Sburlan, S.: Nonlinear mappings of monotone type. Sijthoff & Nordhoff International Publishers, Alphen aan den Rijn (1987)

Reich, S., Tuyen, T.M.: Iterative methods for solving the generalized split common null point problem in Hilbert spaces. Optimization 69(5), 1013–1038 (2020)

Reich, S., Tuyen, T.M., Trang, N.M.: Parallel iterative methods for solving the split common fixed point problem in Hilbert spaces. Numer. Funct. Anal. Optim. 41(7), 778–805 (2020)

Rockafellar, R.T.: On the maximal monotonicity of subdifferential mappings. Pacific J. Math. 33, 209–216 (1970)

Suantai, S., Eiamniran, N., Pholasa, N., Cholamjiak, P.: Three-step projective methods for solving the split feasibility problems. Mathematics 7(8), 712 (2019)

Suantai, S., Pholasa, N., Cholamjiak, P.: Relaxed CQ algorithms involving the inertial technique for multiple-sets split feasibility problems. RACSAM 113, 1081–1099 (2019)

Suantai, S., Kesornprom, S., Cholamjiak, P.: Modified proximal algorithms for finding solutions of the split variational inclusions. Mathematics 7(8), 708 (2019)

Suantai, S., Shehu, Y., Cholamjiak, P.: Nonlinear iterative methods for solving the split common null point problems in Banach spaces. Optim. Meth. Softw. 34, 853–874 (2019)

Suantai, S., Shehu, Y., Cholamjiak, P., Iyiola, O.S.: Strong convergence of a self-adaptive method for the split feasibility problem in Banach spaces. J. Fixed Point Theory Appl. 20, 68 (2018)

Takahashi, W.: Nonlinear Functional Analysis. Yokohama Publishers, Yokohama (2000)

Takahashi, S., Takahashi, W., Toyoda, M.: Strong convergence theorems for maximal monotone operators with nonlinear mappings in Hilbert spaces. J. Optim. Theory Appl. 147(1), 27–41 (2010)

Tang, Y.: New inertial algorithm for solving split common null point problem in Banach spaces. J. Inequal. Appl. 2019, 17 (2019)

Tang, Y.: Convergence analysis of a new iterative algorithm for solving split variational inclusion problems. J. Ind. Manage. Optim. 16(2), 945–964 (2020)

Tang, Y., Gibali, A.: New self-adaptive step size algorithms for solving split variational inclusion problems and its applications. Numer. Algorithms 83, 305–331 (2020)

Tian, M., Jiang, B.N.: Inertial Haugazeau’s hybrid subgradient extragradient algorithm for variational inequality problems in Banach spaces. Optimization. 70(5–6), 987–1007 (2021)

Tuyen, T.M., Thuy, N.T.T., Trang, N.M.: A strong convergence theorem for a parallel iterative method for solving the split common null point problem in Hilbert spaces. J. Optim. Theory Appl. 183(1), 271–291 (2019)

Vinh, N.T., Cholamjiak, P., Suantai, S.: A new CQ algorithm for solving split feasibility problems in Hilbert spaces. Bull. Malays. Math. Sci. Soc. 42, 2517–2534 (2019)

Wang, J., Hu, Y., Yu, C.K.W., Zhuang, X.: A family of projection gradient methods for solving the multiple-sets split feasibility problem. J. Optim. Theory Appl. 183, 520–534 (2019)

Wang, F.: A new method for split common fixed-point problem without priori knowledge of operator norms. J. Fixed Point Theory Appl. 19, 2427–2436 (2017)

Yang, Q.: On variable-step relaxed projection algorithm for variational inequalities. J. Math. Anal. Appl. 302, 166–179 (2005)