Generalized Cesaro Vector-Valued Sequence Space Using Modulus Function

In this paper, we introduced generalized Cesaro vector-valued sequence space X(E, f, Delta(m), p) by taking sequence (E-k, q(k)) of seminormed spaces, modulus function f, m(th)-order difference operator Delta(m) and bounded sequence (p(k)) of strictly positive real numbers. It is proved that the space X(E, f, Delta(m), p) is complete paranormed space if (E-k, q(k)) is a sequence of complete seminormed spaces. Some inclusion relations on the space are obtained. By using composite function f(v), space X(E, f(v), Delta(m), p) is studied for any v is an element of N. A result on multiplier space of X(E, f, Delta(m), p) is also obtained, if m = 0.