Generalized vector-valued paranormed sequence space using modulus function

In this paper we introduce a generalized vector-valued paranormed sequence space N"p(E"k,@D^m,f,s) using modulus function f, where p=(p"k) is a bounded sequence of positive real numbers such that inf"kp"k>0,(E"k,q"k) is a sequence of seminormed spaces with E"k"+"[email protected]?E"k for each k @?N and s>=0. We have also studied sequence space N"p(E"k,@D^m,f^r,s), where f^[email protected][email protected][email protected]?,...,f (r-times composition of f with itself) and [email protected]?N={1,2,3,...}. Results regarding completeness, K-space, normality, inclusion relations etc. are derived. Further, a study of multiplier of the set N"p(E"k,f,s) is also made by choosing (E"k,@[email protected]?"k) as sequence of normed algebras.