A SELF-ADAPTIVE VISCOSITY ALGORITHM FOR SPLIT FIXED POINT PROBLEMS AND VARIATIONAL INEQUALITY PROBLEMS IN BANACH SPACES

In this paper, a new self-adaptive viscosity type algorithm for gener-alized nonexpansive type mappings is introduced to solve the split common fixed point, variational inequality, split common null point, optimization and hierar-chical variational inequality problems. It is shown that the sequence generated by proposed algorithm is strongly convergent to a solution of split common fixed point problem under appropriate conditions and this solution is identified to be the unique solution of a variational inequality problem. A numerical example is presented to illustrate the strength of the proposed approach. The results presented herein improve and generalize various results in the existing literature.