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  • Research Article
  • Open Access

Moduli and Characteristics of Monotonicity in Some Banach Lattices

  • 1,
  • 1Email author,
  • 1 and
  • 2
Fixed Point Theory and Applications20102010:852346

  • Received: 7 December 2009
  • Accepted: 10 February 2010
  • Published:


First the characteristic of monotonicity of any Banach lattice is expressed in terms of the left limit of the modulus of monotonicity of at the point . It is also shown that for Köthe spaces the classical characteristic of monotonicity is the same as the characteristic of monotonicity corresponding to another modulus of monotonicity . The characteristic of monotonicity of Orlicz function spaces and Orlicz sequence spaces equipped with the Luxemburg norm are calculated. In the first case the characteristic is expressed in terms of the generating Orlicz function only, but in the sequence case the formula is not so direct. Three examples show why in the sequence case so direct formula is rather impossible. Some other auxiliary and complemented results are also presented. By the results of Betiuk-Pilarska and Prus (2008) which establish that Banach lattices with and weak orthogonality property have the weak fixed point property, our results are related to the fixed point theory (Kirk and Sims (2001)).


  • Differential Geometry
  • Computational Biology
  • Banach Lattice
  • Full Article
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Authors’ Affiliations

Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland
Institute of Mathematics, Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Prague 1, Czech Republic


© Paweł Foralewski et al. 2010

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.