Some Paranormed Difference Sequence Spaces Derived by Using Generalized Means

TL;DR

This paper introduces new paranormed sequence spaces based on generalized means and difference operators, analyzes their duals and matrix transformations, and studies their geometric properties such as rotundity and Kadec-Klee property.

Contribution

It defines and investigates the properties of new paranormed sequence spaces derived via generalized means and difference operators, including duals, transformations, and geometric features.

Findings

Spaces are complete under a suitable paranorm.

Computed duals and matrix transformation conditions.

Established rotundity and Kadec-Klee property for certain spaces.

Abstract

This paper presents new sequence spaces $X(r, s, t, p ;\Delta)$ for $X \in \{l_\infty(p), c(p), c_0(p), l(p)\}$ defined by using generalized means and difference operator. It is shown that these spaces are complete under a suitable paranorm. Furthermore, the $\alpha$-, $\beta$-, $\gamma$- duals of these sequence spaces are computed and also obtained necessary and sufficient conditions for some matrix transformations from $X(r, s, t, p ;\Delta)$ to $X$. Finally, it is proved that the sequence space $l(r, s, t, p ;\Delta)$ is rotund when $p_n>1$ for all $n$ and has the Kadec-Klee property.