# Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces

@article{Xu1991CharacteristicIO, title={Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces}, author={Zongben Xu and G. F. Roach}, journal={Journal of Mathematical Analysis and Applications}, year={1991}, volume={157}, pages={189-210} }

Abstract Let X be a real Banach space with dual X ∗ and moduli of convexity and smoothness δ X ( e ) and ϱ X ( τ ), respectively. For 1 p denotes the duality mapping from X into 2 X ∗ with gauge function t p − 1 and j p denotes an arbitrary selection for J p . Let A = { φ : R + → + : φ (0) = 0, φ ( t ) is strictly increasing and there exists c > 0 such that φ(t) ⩾ cδ X ( t 2 )} and F = { ϑ : R + → + : ϑ (0) = 0, ϑ ( t ) is convex, nondecreasing and there exists K > 0 such that ϑ ( τ ) ⩽ Kϱ X… Expand

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