By using the resolvent operator due to Lan-Cho-Verma associated with -accretive mappings and the matrix analysis method, we prove the convergence of a new hybrid proximal point three-step iterative algorithm for this system of set-valued variational inclusions and an existence theorem of solutions for this kind of the variational inclusions system.
Using the Resolvent Identity and, we discover (3.39).
Essentially, using the resolvent technique, one can show that the variational inclusions are commensurate to the fixed point problems.
We have established the equivalent between the system of variational inclusions and the fixed point problem using the resolvent operator.
They also studied a class of variational inclusions using the resolvent operator associated with ( A, η ) -accretive mappings.
We establish the equivalence between the general variational inclusions and the fixed point problems as well as with a new class of resolvent equations using the resolvent operator technique.
In [14], Fang and Huang introduced another class of generalized monotone operators, H-monotone operators, defined an associated resolvent operator, established the Lipschitz continuity of the resolvent operator, and studied a class of variational inclusions in Hilbert spaces using the resolvent operator associated with H-monotone operators.
Using the resolvent operator technique, we establish the equivalence between the new system of general variational inclusions and the fixed point problem.
In this section, we establish the equivalence between the general variational inclusion (2.1) and the fixed point problem (3.1) using the resolvent operator technique.
The purpose of this article is to discuss the existence of pseudo almost periodic solutions of linear Volterra equation: x ( n + 1 ) = A ( n ) x ( n ) + ∑ s = - ∞ n F ( n, s ) x ( s ) + p ( n ), n ∈ Z, by using an exponentially stable of the zero solution, which is equivalent to the exponential behaviors of the resolvent matrix G(n, m) as n → ∞ and of some summability of the kernel.
