Iterative algorithms for the split variational inequality and fixed point problems under nonlinear transformations

In the present paper, we consider the split variational inequality and fixed point problem that requires to find a solution of a generalized variational inequality in a nonempty closed convex subset C of a real Hilbert space H whose image under a nonlinear transformation is a fixed point of a pseudocontractive operator. An iterative algorithm is introduced to solve this split problem and the strong convergence analysis is given.