We investigate a new class of cocoercive operators named generalizedH(·,·,·)-η-cocoercive operators in Hilbert spaces. We prove that generalizedH(·,·,·)-η-cocoercive operator is single-valued and Lipschitz continuous and extends the concept of resolvent operators associated withH(·,·)-cocoercive operators to the generalizedH(·,·,·)-η-cocoercive operators. Some examples are given to justify the definition of generalizedH(·,·,·)-η-cocoercive operators. Further, we consider a generalized set-valued variational-like inclusion problem involving generalizedH(·,·,·)-η-cocoercive operator. In terms of the new resolvent operator technique, we give the approximate solution and suggest an iterative algorithm for the generalized set-valued variational-like inclusions. Furthermore, we discuss the convergence criteria of iterative algorithm under some suitable conditions. Our results can be viewed as a generalization of some known results in the literature.
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