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

Abstract

Abstract In this paper, the monotonicity is investigated with respect to Orlicz sequence space l Φ , p $l_{\varPhi , p}$ 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 Φ , p $l_{\varPhi , p}$ . 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 Φ , p $l_{\varPhi , p}$ is calculated.

Keywords

• Orlicz spaces
• Monotonicity
• Monotone coefficient
• p-Amemiya norm