Abstract
Some basic properties in Orlicz spaces and Orlicz sequence spaces that are generated by monotone function equipped with the Mazur-Orlicz F-norm are studied in this paper. We give some relationships between the modulus and the Mazur-Orlicz F-norm. We obtain an interesting result that the norm of an element in line segments is formed by two elements on the unit sphere less than or equal to 1 if and only if that the monotone function is a convex function. The criterion that Orlicz spaces and Orlicz sequence spaces that are generated by monotone function equipped with the Mazur-Orlicz F-norm are strictly monotone or lower locally uniform monotone is presented.
Highlights
Geometry of Banach space has important applications in the control theory, fixed-point theory, ergodic theory, probability theory, and vector analytic function theory
It is well known that monotonicity properties play an analogous role in the best dominated approximation problems in Banach lattices as the respective rotundity properties in the best approximation problems in Banach spaces
Monotonicity properties are applicable in the ergodic theory, since they provide a tool for estimating a norm
Summary
Geometry of Banach space has important applications in the control theory, fixed-point theory, ergodic theory, probability theory, and vector analytic function theory. If Φ is right continuous and X is a Banach space, increasing function on 1⁄20, +∞ such that Φð0Þ = 0. By lim ΦðuÞ = 0, for any ε > 0, there exists δ > 0 such that u→0+0
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
