On lacunary strong invariant convergence with order

Abstract

We known that the most vital part of summability theory is the
sequence spaces. In this paper by using a modulus and the $\rho$- function we shall introduce the new sequence space of order $\gamma$ which is defined below. In our
work, we mainly focus on improve and
generalize several existing results on sequence spaces. We should strongly indicate that our new sequence space is more general than
that of corresponding sequence space defined by Waszak, \cite{WA}. Furthermore we establish some inclusion relations among the these sequence spaces in some detail.