Journal of Function Spaces (Jan 2020)

Local Uniform Kadec-Klee Property (LUKK) and Modulus of (LUKK)

  • Yunan Cui,
  • Xiaoxia Wang

DOI
https://doi.org/10.1155/2020/8191878
Journal volume & issue
Vol. 2020

Abstract

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A new geometry property and two new moduli are introduced in Banach space. First, the concept of local uniform Kadec-Klee property (LUKK) is introduced and the implication relationships between LUKK and local near uniform convexity LNUC, uniformly Kadec-Klee (UKK), (H) are investigated in Banach space. Furthermore, the modulus PXLε of (LUKK) and the modulus ΔXLε of LNUC are introduced and the relationship of size between PXLε and ΔXLε is also investigated in Banach space. Finally, several formulas for PXLε are calculated in classical Banach space lp.