Generalized H(·,·,·)‎-η-Cocoercive Operators and Generalized Set-Valued Variational-Like Inclusions

Abstract EN

We investigate a new class of cocoercive operators named generalized H(·,·,·)-η-cocoercive operators in Hilbert spaces.

We prove that generalized H(·,·,·)-η-cocoercive operator is single-valued and Lipschitz continuous and extends the concept of resolvent operators associated with H(·,·)-cocoercive operators to the generalized H(·,·,·)-η-cocoercive operators.

Some examples are given to justify the definition of generalized H(·,·,·)-η-cocoercive operators.

Further, we consider a generalized set-valued variational-like inclusion problem involving generalized H(·,·,·)-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.