common solution of a combination of split general variational-like inequality problems and a family of generalized asymptotically nonexpansive mappings

We suggest and analyze an iterative method to approximate a common solution of a combination of split general variational-like inequality problems and a common fixed point problem for a family of generalized asymptotically nonexpansive nonself mappings by using a specific way of choosing the indexes of the involved mappings. further, we prove that sequences generated by the proposed iterative algorithm converge strongly to a common solution of these problems. the results presented in this paper generalize and unify some known related results in the literature.