Abstract
In this paper, we define a generalized modular sequence space by using the generalized de la Vallée-Poussin mean with a generalized Riesz transformation. Moreover, we investigate the property and the uniform Opial property which is equipped with the Luxemburg norm. Finally, we show that this space has the fixed point property.
Highlights
1 Introduction A number of mathematicians are studying the geometric properties of Banach spaces, because such properties were identified as an important characteristic of the Banach spaces
In, Şimşek et al [ ] introduced a new modular sequence space which is more general than the Cesàro sequence space defined by Shiue [ ] and the generalized Cesàro sequence space defined by Suantai
The main purpose of this paper is to investigate the property (β) and the uniform Opial property equipped with the Luxemburg norm of the new modular sequence space, which is defined by using the generalized de la Vallée-Poussin mean with generalized Riesz transformation
Summary
Space defined by Shiue [ ] and the generalized Cesàro sequence space defined by Suantai. In , Mongkolkeha and Kumam [ ] defined the generalized Cesàro sequence space ces(p)(q) for a bounded sequence p = (pk) with pk ≥ for all k ∈ N and q = (qk) of positive real numbers. Şimşek et al [ , ] defined it by the modular sequence space with de la Vallée-Poussin’s mean and studied some geometric properties in these spaces. The generalized Cesàro sequence space ces(p) for p = (pk) a bounded sequence of positive real numbers with pk ≥ for all k ∈ N of Suantai [ , ] is defined by ces(p) = x ∈ l : (λx) < ∞ for some λ > , where. The modular sequence space V (λ; p) of Şimşek et al [ , ] is defined by de la ValléePoussin’s mean, namely
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.
