Local monotonicity coefficients in Orlicz sequence spaces equipped with the p -Amemiya norm

[摘要] In this paper, the monotonicity is investigated with respect to Orlicz sequence space $l_{\varPhi , p}$ 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 $l_{\varPhi , p}$ . 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, $l_{\varPhi , p}$ is calculated.

[学科分类] 电力

[关键词] Orlicz spaces;Monotonicity;Monotone coefficient;p -Amemiya norm