A new generalized vector-valued paranormed sequence space using modulus function

Tanweer Jalala, * and Reyaz Ahmadb

A new generalized vector-valued paranormed sequence space using modulus function

Authors :

Tanweer Jalal^{a, *} and Reyaz Ahmad^b

Author Address :

^a Associate Professor, Department of General Studies, Yanbu Industrial College, P.O. Box: 30436, Yanbu Al-Saniayaiah, Kingdom of Saudia Arabia.
^bDepartment of Mathematics, NIT-Srinagar, INDIA.

**Corresponding author.

Abstract :

In this paper we introduce a new generalized vector-valued paranormed sequence spaces $N_p(E_k, riangle_u^m,f,s)$ using modulus function $f$, where $p=(p_k)$ is a bounded sequence of positive real numbers such that $inf _{k}p_{k}>0, (E_k,q_k)$ is a sequence of seminormed spaces with $E_{k+1}subseteq E_k$ for each $kin N$ and $sgeq 0$. We prove results regarding completeness, $K$-space, normality, inclusion relation are derived. These are more general than those of Ruckle [7], Maddox [5], Ozturk and Bilgin [6], Sahiner [8], Atlin {it et al.} [1] and Srivastava and Kumar [9].

Keywords :

Modulus function, paranormed space, normal sequence space, difference sequence space.

DOI :

Article Info :

Received : March 07, 2014; Accepted : August 23, 2014.