Resolvent Operator Method for General Variational Inclusions
نویسنده
چکیده
In this paper, we introduce a new class of variational inclusions involving three operator. Using the resolvent operator technique, we establish the equivalence between the general variational inclusions and the resolvent equations. We use this alternative equivalent formulation to suggest and analyze some iterative methods for solving the general variational inclusions. We also consider the criteria of these iterative methods under suitable conditions. Since the general variational inclusions include the variational inequalities and the related optimization problems as special cases, our results continue to hold for these problems. Mathematics subject classification (2000): 49J40, 90C33.
منابع مشابه
A System of Nonlinear Variational Inclusions with General H-monotone Operators in Banach Spaces
A system of nonlinear variational inclusions involving general H-monotone operators in Banach spaces is introduced. Using the resolvent operator technique, we suggest an iterative algorithm for finding approximate solutions to the system of nonlinear variational inclusions, and establish the existence of solutions and convergence of the iterative algorithm for the system of nonlinear variationa...
متن کاملGeneralized ( a , Η ) − Resolvent Operator Technique and Sensitivity Analysis for Relaxed Cocoercive Variational Inclusions
Sensitivity analysis for relaxed cocoercive variational inclusions based on the generalized resolvent operator technique is discussed The obtained results are general in nature.
متن کاملFuzzy Multivalued Variational Inclusions in Banach Spaces
The purpose of this paper is to introduce the concept of general fuzzy multivalued variational inclusions and to study the existence problem and the iterative approximation problem for certain fuzzy multivalued variational inclusions in Banach spaces. Using the resolvent operator technique and a new analytic technique, some existence theorems and iterative approximation techniques are presented...
متن کاملExplicit Parallel Resolvent Methods for System of General Variational Inclusions
In this paper, we introduce and consider a new system of extended general variational inclusions involving eight different operators. Using the resolvent operator techniques, we show that the new system of extended general variational inclusions is equivalent to the fixed point problem. We prove the strong convergence of some new explicit iterative parallel algorithms using resolvent methods un...
متن کاملSystem of Mixed Variational-Like Inclusions and -Proximal Operator Equations in Banach Spaces
In this paper, we introduce and study a system of mixed variational-like inclusions and a system of proximal operator equations in Banach spaces which contains variational inequalities, variational inclusions, resolvent equations, system of variational inequalities and system of variational inclusions in the literature as special cases. It is established that the system of mixed variational-lik...
متن کامل