On the geometric properities of new type modular space

In this paper, using a modular, we have defined the modular space $M_{m^*}(p)$ and we have shown that the sequence space $M_{m^*}(p)$ equipped with the Luxemburg norm is rotund and possesses H-property (or Kadec-Klee property) when $p=(p_k)$ is bounded with $p_k>1$ for all $kinmathbb{N}$.