H ((·,·),(·,·)) -mixed cocoercive operators with an application for solving variational inclusions in Hilbert spaces

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. © 2013 shamshad husain and sanjeev gupta.