Abstract
It is well known that the modulus of nearly uniform smoothness related with the fixed point property is important in Banach spaces. In this paper, we prove that the modulus of nearly uniform smoothness in Köthe sequence spaces without absolutely continuous norm is ΓX(t)=t. Meanwhile, the formula of the modulus of nearly uniform smoothness in Orlicz sequence spaces equipped with the Luxemburg norm is given. As a corollary, we get a criterion for nearly uniform smoothness of Orlicz sequence spaces equipped with the Luxemburg norm. Finally, the equivalent conditions of R(a,l(Φ))<1+a and RW(a,l(Φ))<1+a are given.
Highlights
In last century, the fixed point property has been studied by many scholars
It is well known that the modulus of nearly uniform smoothness related with the fixed point property is important in Banach spaces
We prove that the modulus of nearly uniform smoothness in Kothe sequence spaces without absolutely continuous norm is ΓX(t) = t
Summary
The fixed point property has been studied by many scholars. A Banach space X is said to have the fixed point property (FPP, for short) if every nonexpansive mapping T : C → CTx − Ty ≤ x − y , ∀x, y ∈ C (1)acting on a nonempty bounded closed and convex subset C of X has a fixed point. It is well known that the modulus of nearly uniform smoothness related with the fixed point property is important in Banach spaces. We prove that the modulus of nearly uniform smoothness in Kothe sequence spaces without absolutely continuous norm is ΓX(t) = t. The formula of the modulus of nearly uniform smoothness in Orlicz sequence spaces equipped with the Luxemburg norm is given.
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.
