Mixed variational-like inclusions and J η-proximal operator equations in Banach spaces ✩

In this paper, we study mixed variational-like inclusions and J η-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 J η-proximal operator equations. This equivalence is used to suggest an iterative algorithm for solving J η-proximal operator equations. © 2006 Elsevier Inc. All rights reserved.