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Journal of Convex Analysis 16 (2009), No. 2, 487--499
Copyright Heldermann Verlag 2009

Some Quantitative Interpolation Theorems under Lions-Peetre's Methods

Ming Fan
School of Industrial Technology and Management, Dalarna University, 781 88 Borlänge, Sweden

We formulate the quantitative version of interpolation theorems on compactness and weak compactness, the improved estimate for the k-uniform rotundity, and even the stability of the nearly uniform convexity under Lions-Peetre's interpolation methods of constants and means associated with quasi-power function parameters.

Keywords: Interpolation, k-uniform rotundity, Lions-Peetre's method, nearly uniform convexity, noncompactness, weak noncompactness.

MSC: 46B70, 46M35; 46B50, 47B07

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