Abstract
We introduce new sequence space involving lacunary sequence connected with Cesaro sequence space and examine some geometric properties of this space equipped with Luxemburg norm.
Highlights
Let (X, · ) be a real Banach space and let B(X)(resp., S(X)) be the closed unit ball of X
We introduce the new sequence space l(p,θ) involving lacunary sequence as follows: l(p,θ) =
In [9], it is shown that the space ces(p) equipped with the Luxemburg norm is not rotund nor locally uniformly rotund (LUR)
Summary
Let (X, · ) be a real Banach space and let B(X)(resp., S(X)) be the closed unit ball (resp., the unit sphere) of X. A point x ∈ S(X) is an H-point of B(X) if for any sequence (xn) in X such that xn →1 as n→∞, weak convergence of (xn) to x (write xn →w x) implies that xn − x →0 as n→∞. If every point in S(X) is an H-point of B(X), X is said to have the property (H). A point x ∈ S(X) is a locally uniformly rotund point of B(X)(LUR-point) if for any sequence (xn) in B(X) such that xn + x →2 as n→∞, there holds xn − x →0 as n→∞. A Banach space X is said to be rotund (R) if every point of S(X) is an extreme point of B(X). If every point of S(X) is an LUR-point of B(X), X is said to be locally uniformly rotund (LUR). The space of lacunary strongly convergent sequences Nθ was defined by Freedman et al [12] as
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.
