Product formulas, nonlinear semigroups, and accretive operators

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...

Regularization of Nonlinear Ill-posed Equations with Accretive Operators

We study the regularization methods for solving equations with arbitrary accretive operators. We establish the strong convergence of these methods and their stability with respect to perturbations of operators and constraint sets in Banach spaces. Our research is motivated by the fact that the fixed point problems with nonexpansive mappings are namely reduced to such equations. Other important ...

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.

Sharp Convergence Rates for Nonlinear Product Formulas

Nonlinear versions of the Lie-Trotter product formula exp[t(A + B)] = \im„^x[exp((t/n)A)exp((t/n)B)}" and related formulas are given in this paper. The convergence rates are optimal. The results are applicable to some nonlinear partial differential equations. 0. Introduction. The Lie-Trotter product formula states that (0.1) exp(^)exp(^)exp(^C e,(A + B+c) asn^oo. (The exponent n indicates itera...

Semigroup Product Formulas and Addition of Unbounded Operators