The present research is an attempt to define a class of generalized α i β j-(H p , φ)-η-accretive mappings as well as it is a study of its associated class of proximal-point mappings. The generalized α i β j-(H p, φ)-η-accretive mappings is the sum of two symmetric accretive mappings and an extension of the generalized αβ-H(., .)-accretive mapping [28]. Further the research is a discussion on graph convergence of generalized α i β j-(H p, φ)-η-accretive mappings and its application includes a set-valued variational-like inclusion problem (SVLIP, in short) in semi inner product spaces. Furthermore an iterative algorithm is proposed, and an attempt is made to discuss the convergence analysis of the sequences generated from the proposed iterative algorithm. An example is constructed that demonstrate few graphics for the convergence of proximal-point mapping. Our results can be viewed as a refinement and generalization of some known results in the literature.