A new general iterative scheme for split variational inclusion and fixed point problems of k-strict pseudo-contraction mappings with convergence analysis

Strong convergence theorem for split monotone variational inclusion with constraints of variational inequalities and fixed point problems

“…It is worth stressing that the parameter λ of resolvent operators and in many results is the same λ ; see, e.g., [1, 11–13]. Thus our result improves and extends these results and other related results.…”

“…Compared with Theorem 3.1 of Jitsupa et al [1], our result is different from it in the following aspects: We not only change the parameter λ of resolvent operators and into different parameters and , but also change the resolvent operator into which is more general than . It is worth stressing that the parameter λ of resolvent operators and in many results is the same λ ; see, e.g., [1, 11–13].…”

“…We notice that Jitsupa et al [1] did not define the domains and the ranges of and in the iteration process (1.6) and Theorem 3.1 of [1]. Certainly, it is easy to misunderstand that is defined on into and is defined on into .…”

“…Very recently, Jitsupa et al [1] modified algorithm (1.5) for SVIP (1.2) and the fixed point problem of a finite family of strict pseudo-contractions: where A is a bounded linear operator, is the adjoint of A , is a finite family of -strictly pseudo-contractions, f is a contraction, D is a strong positive linear bounded operator. They proved, under certain appropriate assumptions on the sequences , , and , that defined by (1.6) converges strongly to a common solution of SVIP (1.2) and a fixed point of a finite family of -strictly pseudo-contractions, which solves some variational inequality problem.…”

“…Math. 318:293–306, 2017), we propose a general iterative scheme for finding a solution of a split monotone variational inclusion with the constraints of a variational inequality and a fixed point problem of a finite family of strict pseudo-contractions in real Hilbert spaces. Under very mild conditions, we prove a strong convergence theorem for this iterative scheme.…”