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

Abstract

In this paper we introduce a new generalized vector-valued paranormed sequence spaces \(N_p\left(E_k, \triangle_u^m, f, s\right)\) using modulus function \(f\), where \(p=\left(p_k\right)\) is a bounded sequence of positive real numbers such that \(\inf _k p_k>\) \(0,\left(E_k, q_k\right)\) is a sequence of seminormed spaces with \(E_{k+1} \subseteq E_k\) for each \(k \in N\) and \(s \geq 0\). 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 et al. [1] and Srivastava and Kumar [9].