Tikhonov regularization in Banach spaces—improved convergence rates results

In this paper, we deal with convergence rates for a Tikhonov-like regularization approach for linear ill-posed problems in Banach spaces. Here, we deal with the so-called distance functions which quantify the violation of an introduced reference source condition. Under validity of this reference source condition we derive convergence rates which are well-known as optimal in a Hilbert space situation. Additionally, we present error bounds and convergence rates which are based on the decay rate of the distance functions when the reference source condition is violated.

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