Mixed variational-like inclusions and Jη-proximal operator equations in Banach spaces

In this paper, we study mixed variational-like inclusions and Jη-proximal operator equations in Banach spaces. It is established that mixed variational-like inclusions in real Banach spaces are equivalent to fixed point problems. We also establish a relationship between mixed variational-like inclusions and Jη-proximal operator equations. This equivalence is used to suggest an iterative algorithm for solving Jη-proximal operator equations.