Two problems of approximation in Hilbert spaces are considered with one additional equality condition: the smoothing problem with a weight and the smoothing problem with an obstacle. This condition is a generalization of the equality, which appears in the problem of approximation of a histogram in a natural way. We characterize the solutions of these smoothing problems and investigate the connection between them.
Asmuss, S., & Budkina, N. (2009). On smoothing problems with one additional equality condition. Mathematical Modelling and Analysis, 14(2), 159-168. https://doi.org/10.3846/1392-6292.2009.14.159-168
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