Uniformly a posteriori error estimates for regularizing algorithms

A modification for the definition of an a posteriori error estimate for a regularizing algorithm for solving an ill-posed problem is proposed. We introduce, analyze and illustrate by examples the concept of a uniformly a posteriori error estimate for a regularizing algorithm. A necessary and sufficient condition for the existence of a regularizing algorithm satisfying such an estimate is established. The class of conditionally well-posed problems is characterized in terms of regularizability with uniformly a posteriori error estimates.