H(.,.)−η -cocoercive operators and variational-like inclusions in Banach spaces

In this paper, we define H(.,.)−η-cocoercive operators in q-uniformly smooth Banach spaces and its resolvent operator. We prove the Lipschitz continuity of the resolvent operator associated with H(.,.)−η-cocoercive operator and estimate its Lipschitz constant. By using the techniques of resolvent operator, an iterative algorithm for solving a variational-like inclusion problem is constructed. The existence of solution for the variational-like inclusions and the convergence of iterative sequences generated by the algorithm is proved. Some examples are given.