This work aims to develop a new class of accretive mappings and investigate its associated class of proximal mappings. This new class of accretive mappings is known as generalized (Hk,φ)-η-accretive mappings. Further, the research work includes a discussion of its application, leading to set-valued variational-like inclusions (SVVLI, in short) in the semi-inner product spaces. The corresponding fixed point problem for SVVLI is given. This fixed point problem is used to provide an iterative scheme for solving SVVLI. Furthermore, we study the convergence analysis of the suggested iterative method. An illustration is built in support of our result.