Document Type : Research Articles


1 Department of Management Studies, Indian Institute of Technology, Madras, Chennai 600 036, Tamil Nadu, India. email:

2 Mathematics Discipline, PDPM Indian Institute of Information Technology, Design and Manufacturing, Jabalpur, P.O.: Khamaria, Jabalpur 482 005, Madhya Pradesh, India. , email:

3 Department of Mathematics, SASTRA University, Thanjavur-613 401, India, email:

4 Dept. of Math., Lovely Prof. Univ. Jalandhar-Delhi G.T. Road, Phagwara, Punjab 144 411, India, L.1627 Awadh Puri Colony Beniganj, Phase-III, Opposite-Industrial Training Institute (I.T.I.), Ayodhya Main Road Faizabad 224 001,


In this article, we define the vector valued multiple of $\chi^{2}$ over $p$-metric sequence spaces defined by Musielak and study some of their topological properties and some inclusion results.