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}
}
  • Zongben Xu, G. Roach
  • Published 1991
  • Mathematics
  • Journal of Mathematical Analysis and Applications
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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let X be a real uniformly convex and uniformly smooth Banach space. For any 1<p<∞, J p ,J p * respectively denote the duality mapping with gauge function φ(t)=t p−1 from X onto X * and S * onto X. IfExpand
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Suppose T is a multivalued monotone operator (not necessarily continuous) with open domain D(T) in Lp (2⩽p-∞), f ∈ R(I + T) and the equation f ∈ x + Tx has a solution q ∈ D(T). Then there exists aExpand
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Springer-Verlag is reissuing a selected few of these highly successful books in a new, inexpensive sofcover edition to make them easily accessible to younger generations of students and researchers. Expand
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