Strong convergence theorems of general split equality problems for quasi-nonexpansive mappings

The purpose of this paper is to introduce and study the general split equality problem and general split equality fixed point problem in the setting of infinite-dimensional Hilbert spaces. Under suitable conditions, we prove that the sequences generated by the proposed new algorithm converges strongly to a solution of the general split equality fixed point problem and the general split equality problem for quasi-nonexpansive mappings in Hilbert spaces. As an application, we shall utilize our results to study the null point problem of maximal monotone operators, the split feasibility problem, and the equality equilibrium problem. The results presented in the paper extend and improve the corresponding results announced by Moudafi et al. (Nonlinear Anal. 79:117-121, 2013; Trans. Math. Program. Appl. 1:1-11, 2013), Eslamian and Latif (Abstr. Appl. Anal. 2013:805104, 2013) and Chen et al. (Fixed Point Theory Appl. 2014:35, 2014), Censor and Elfving (Numer. Algorithms 8:221-239, 1994), Censor and Segal (J. Convex Anal. 16:587-600, 2009) and some others.