Abstract
We introduce the notion of (α,β)-norm in the spaceL p(t) of functionsx(t) for which
wherep(t) is a positive measurable function. We establish a criterion for the element of the best (α,β)-approximation in the spaceL p(t). We obtain inequalities of the type of duality relations.
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Additional information
Dnepropetrovsk University, Dnepropetrovsk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 7., pp. 952–959, July, 1999.
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Polyakov, O.V., Litvin, E.G. Asymmetric approximations in the spaceL p(t) . Ukr Math J 51, 1069–1078 (1999). https://doi.org/10.1007/BF02592042
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DOI: https://doi.org/10.1007/BF02592042