Split common fixed point problem of nonlinear operator with application

‎In this paper‎, ‎we present a new general algorithm for solving‎ ‎the split common fixed point problem in an infinite dimensional‎ ‎Hilbert space‎, ‎which is to find a point which belongs to the‎ ‎common fixed point of a family of demicontractive mappings‎ ‎such that its image under two linear transformations belong to the‎ ‎common fixed point of another families of demicontractive mappings in the image space‎. ‎We establish the strong convergence‎ ‎for the algorithm to find a unique solution of the variational‎ ‎inequality‎, ‎which is the optimality condition for the minimization‎ ‎problem‎. ‎The algorithm and its convergence results improve and‎ ‎develop previous results in this field‎