A New Paranormed Space Derived by Jordan Totient Function and Characterizations of Some Matrix Transformations
Year: 2025
Type: article
Abstract: Paranormed linear spaces have many important properties, since they appear as the generalization of normed linear spaces. The most well-known the paranormed linear space among these spaces is ℓ(p) linear space of the sequences x=(x_{k}) satisfying ∑_{k=0}^{∞}|x_{k}|^{p_{k}}<∞ , which was defined by Maddox in 1967. The main purpose of this study is to introduce a new paranormed space |Υ_{u}^{r}|(p) over the paranormed space ℓ(p) using the Jordan totient mean that is well-known arithmetic function in number theory, where p=(p_{k}) is a bounded sequence of positive real numbers. Besides this, we investigate some topological properties and compute the α-,β-, and γ- duals of this paranormed space. Finally, we characterize the classes of infinite matrices (|Υ_{u}^{r}|(p),λ) and (λ,|Υ_{u}^{r}|(p)), where λ is any given sequence space.
Authors: Canan Hazar Güleç, Özlem Girgin Atlıhan
Institution: Pamukkale University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7117731083