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Abstract
Tikhonov regularization in Banach spaces with convex penalty and convex fidelity term for linear ill-posed operator equations is studied. As a main result, convergence rates in terms of the Bregman distance of the regularized solution to the exact solution is proven by imposing a generalization of the established variational inequality conditions on the exact solution. This condition only involves a decay rate of the difference of the penalty functionals in terms of the residual.
The author would like to thank Elena Resmerita for productive discussions.
Received: 2015-4-1
Revised: 2015-6-1
Accepted: 2015-7-28
Published Online: 2015-8-29
Published in Print: 2016-6-1
© 2016 by De Gruyter