Abstract
AbstractIn this paper, the monotonicity is investigated with respect to Orlicz sequence space $l_{\varPhi , p}$
l
Φ
,
p
equipped with the p-Amemiya norm, and the necessary and sufficient condition is obtained to guarantee the uniform monotonicity, locally uniform monotonicity, and strict monotonicity for $l_{\varPhi , p}$
l
Φ
,
p
. This completes the results of the paper (Cui et al. in J. Math. Anal. Appl. 432:1095–1105, 2015) which were obtained for the non-atomic measure space. Local upper and lower coefficients of monotonicity at any point of the unit sphere are calculated, $l_{\varPhi , p}$
l
Φ
,
p
is calculated.
Funder
China Natural Science Fund under grant
the Fundamental Research Funds for the Central Universities
National Natural Science Foundation of China
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Reference38 articles.
1. Cui, Y.A., Hudzik, H., Wisła, M.: Monotonicity properties and dominated best approximation problems in in Orlicz spaces equipped with the p-Amemiya norm. J. Math. Anal. Appl. 432, 1095–1105 (2015)
2. Akcoglu, M.A., Sucheston, L.: On uniform monotonicity of norms and ergodic theorems in function spaces. Rend. Circ. Mat. Palermo 8(2), 325–335 (1985)
3. Birkhoff, G.: Lattice Theory. Am. Math. Soc., Providence (1979)
4. Betiuk-Pilarska, A., Prus, S.: Banach lattices which are order uniformly noncreasy. J. Math. Anal. Appl. 342(2), 1271–1279 (2008)
5. Chen, S.T., He, X., Hudzik, H.: Monotonicity and best approximation in Banach lattices. Acta Math. Sin. 5(25), 785–794 (2009)