Difference Sequence Spaces Derived by Using Generalized Means

TL;DR

This paper introduces new sequence spaces constructed via generalized means and difference operators, demonstrating their completeness, basis properties, duals, and conditions for matrix transformations.

Contribution

It defines and analyzes new sequence spaces using generalized means and difference operators, including their basis, duals, and transformation criteria.

Findings

Spaces are complete normed linear spaces.

Spaces for c and c0 have Schauder basis.

Duals and matrix transformation conditions are established.

Abstract

This paper deals with new sequence spaces $X(r, s, t ;\Delta) $ for $X\in \{l_\infty, c, c_0\}$ defined by using generalized means and difference operator. It is shown that these spaces are complete normed linear spaces and the spaces $X(r, s, t ;\Delta)$ for $X\in \{c, c_0\}$ have Schauder basis. Furthermore, the $\alpha$-, $\beta$-, $\gamma$- duals of these sequence spaces are computed and also established necessary and sufficient conditions for matrix transformations from $X(r, s, t ;\Delta)$ to $X$.