Abstract
In this paper points of lower strict monotonicity, upper strict monotonicity, lower local uniform monotonicity and upper local uniform monotonicity of Orlicz function spaces equipped with a Mazur–Orlicz F-norm and generated by a monotone (non-convex in general) Orlicz function are studied. We show that both the necessary and sufficient conditions and the suitable theorems are formulated in full generality. Moreover, lower (upper) strict monotonicity and lower (upper) local uniform monotonicity theorems of the paper https://doi.org/10.1007/s00010-018-0615-y are revealed as corollaries in this paper.
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Acknowledgements
We are very grateful to the reviewer for good suggestions in the paper. Your suggestions greatly improved the accuracy and completeness of the manuscript. We would like to extend our gratitude to all of the experts who dedicated their time and expertise to the paper.
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Funding was provided by National Natural Science Foundation of China (Grant No. 11871181).
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Yang, Y., Cui, Y. & Kaczmarek, R. Points of monotonicity in F-normed Orlicz function spaces. Aequat. Math. 97, 659–682 (2023). https://doi.org/10.1007/s00010-023-00961-2
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DOI: https://doi.org/10.1007/s00010-023-00961-2
Keywords
- Orlicz space
- Mazur–Orlicz F-norm
- Points of lower (upper) strict monotonicity
- Points of lower (upper) local uniform monotonicity