Totally 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.

Nonlinear Accretive Operators in Banach Spaces by Felix E. Browder

for each * in X. For any Banach space X and any element * of Xt J(x) is a nonempty closed convex subset of the sphere of radius ||x|| about zero in X*. If X* is strictly convex, J is a singlevalued mapping of X into X* and is continuous from the strong topology of X to the weak* topology of X*. J is continuous in the strong topologies if and only if the norm in X is C on the complement of the o...

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...

Cauchy Problems for Functional Evolution Inclusions Involving Accretive Operators

We study the existence and stability of solutions for a class of nonlinear functional evolution inclusions involving accretive operators. Our approach is employing the fixed point theory for multivalued maps and using estimates via the Hausdorff measure of noncompactness.

On the Sum of Fractional Derivatives and M-accretive Operators