Surjectivity of $\varphi $-accretive operators

Φ-strongly Accretive Operators

Suppose that X is an arbitrary real Banach space and T : X → X is a Lipschitz continuous φ-strongly accretive operator or uniformly continuous φ-strongly accretive operator. We prove that under different conditions the three-step iteration methods with errors converge strongly to the solution of the equation Tx = f for a given f ∈ X.

On surjectivity of some classes of generalized monotone operators

We present results for the existence of solutions for variational inequalities given by generalized monotone operators. As a consequence we establish surjectivity, and we obtain, in particular, results for the existence of zeroes of some class of set-valued operators. Furthermore, by strengthening the continuity assumption on the operator, we deduce its surjectivity without any monotonicity ass...

Stability of Stationary Transport Equations with Accretive Collision Operators

In this paper we consider transport equations with accretive collision operators. We characterize when the equation has a unique solution and show that in this case the solution is stable under small perturbations of the collision operator and the initial value. In one case in which there is more than one solution we show how to make a special selection of a solution, which is then stable again...

Numerical Approximation of Fractional Powers of Regularly Accretive Operators

We study the numerical approximation of fractional powers of accretive operators in this paper. Namely, if A is the accretive operator associated with an accretive sesquilinear form A(·, ·) defined on a Hilbert space V contained in L(Ω), we approximate A for β ∈ (0, 1). The fractional powers are defined in terms of the so-called Balakrishnan integral formula. Given a finite element approximatio...

On the Sum of Fractional Derivatives and M-accretive Operators