A new paranormed space derived from the Jordan totient function and characterizations of some matrix transformations

OpenAlex İngilizce

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.