H((·,·)‎,(·,·)‎)‎-Mixed Cocoercive Operators with an Application for Solving Variational Inclusions in Hilbert Spaces

Abstract EN

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

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

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

Further, by using resolvent operator technique, we discuss the approximate solution and suggest an iterative algorithm for the generalized mixed variational inclusions involving H((·,·),(·,·))-mixed cocoercive operators in Hilbert spaces.

We also discuss the convergence criteria for the iterative algorithm under some suitable conditions.

Our results can be viewed as a generalization of some known results in the literature.