arXiv subjects

Amit Maji

Publications and source records attributed to Amit Maji.

22 records · Page 2Linked to original sources

arXiv2013

Some $B$-Difference Sequence Spaces Derived by Using Generalized Means and Compact Operators

This paper presents new sequence spaces $X(r, s, t, p ; B)$ 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 paranormed spaces and the spaces $X(r, s, t, p ; B)$ for $X \in \{c(p), c_0(p), l(p)\}$ have Schauder basis. Furthermore, the $α$-, $β$-, $γ$- duals of these sequence spaces are computed and also obtained necessary and sufficient conditions for some matrix transformations from $X(r, s, t, p ;B)$ to $X$. Finally, some classes of compact operators on the space $l_p(r, s, t ;B)$ are characterized by using the Hausdorff measure of noncompactness.

math.FA↗

arXiv2013

"Some $m$th-order Difference Sequence Spaces of Generalized Means and Compact Operators"

In this paper, new sequence spaces $X(r, s, t ;Δ^{(m)})$ for $X\in \{l_\infty, c, c_0\}$ defined by using generalized means and difference operator of order $m$ are introduced. It is shown that these spaces are complete normed linear spaces and the spaces $c_0(r, s, t ;Δ^{(m)})$, $c(r, s, t ;Δ^{(m)})$ have Schauder basis. Furthermore, the $α$-, $β$-, $γ$- duals of these spaces are computed and also obtained necessary and sufficient conditions for some matrix transformations from $X(r, s, t ;Δ^{(m)})$ to $X$. Finally, some classes of compact operators on the spaces $c_0(r, s, t ;Δ^{(m)})$ and $l_{\infty}(r, s, t ;Δ^{(m)})$ are characterized by using the Hausdorff measure of noncompactness.

math.FA↗

arXiv2013

Difference Sequence Spaces Derived by Using Generalized Means

This paper deals with new sequence spaces $X(r, s, t ;Δ) $ 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 $X(r, s, t ;Δ)$ for $X\in \{c, c_0\}$ have Schauder basis. Furthermore, the $α$-, $β$-, $γ$- duals of these sequence spaces are computed and also established necessary and sufficient conditions for matrix transformations from $X(r, s, t ;Δ)$ to $X$.

math.FA↗

arXiv2013

Some Paranormed Difference Sequence Spaces Derived by Using Generalized Means

This paper presents new sequence spaces $X(r, s, t, p ;Δ)$ 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 $α$-, $β$-, $γ$- duals of these sequence spaces are computed and also obtained necessary and sufficient conditions for some matrix transformations from $X(r, s, t, p ;Δ)$ to $X$. Finally, it is proved that the sequence space $l(r, s, t, p ;Δ)$ is rotund when $p_n>1$ for all $n$ and has the Kadec-Klee property.

math.FA↗