Analysis in Theory and Applications Anal. Theory Appl., Vol. 30, No. 2 (2014), pp. 214-223 DOI: 10.4208/ata.2014.v30.n2.7 On Some Class of n-Normed Generalized Difference Sequences Related to ℓ p -Space Binod Chandra Tripathy 1, ∗ , Inder Kumar Rana 2 and Stuti Borgohain 2 1 Mathematical Sciences Division, Institute of Advanced Study in Science and Technology, Paschim Boragaon, Garchuk, GUWAHATI-781035, India 2 Department of Mathematics, Indian Institute of Technology, Powai, MUMBAI 400 076, India Received 10 December 2013; Accepted (in revised version) 27 February 2014 Available online 30 June 2014 Abstract. In this paper, we introduce the class of n-normed generalized difference se- quences related to ℓ p -space. Some properties of this sequence space like solidness, symmetricity, convergence-free etc. are studied. We obtain some inclusion relations involving this sequence space. Key Words: Generalized difference operator, n-norm, n-Banach space, symmetricity, solidness, convergence free, completeness. AMS Subject Classifications: 40A05, 40A25, 40A30, 40C05 1 Introduction The notion of n-normed space was studied at the initial stage by Gahler [7], Misiak [10], Gunawan [8] and many others from different aspects. Let n ∈ N and X be a real vector space. A real valued function on X n satisfying the following ‖·, ···‖ four properties: 1. ‖(z 1 , z 2 , ··· , z n )‖ n = 0 if and only if z 1 , z 2 , ··· , z n are linearly dependent; 2. ‖(z 1 , z 2 , ··· , z n )‖ n is invariant under permutation; 3. ‖(z 1 , z 2 , ··· , z n−1 , αz n )‖ n = ‖α‖‖(z 1 , z 2 , ··· , z n )‖ n , for all α ∈ R; 4. ‖(z 1 , z 2 , ··· , z n−1 , x + y)‖ n ≤‖(z 1 , z 2 , ··· , z n−1 , x)‖ n + ‖(z 1 , z 2 , ··· , z n−1 , y)‖ n ; ∗ Corresponding author. Email addresses: tripathybc@yahoo.com (B. C. Tripathy), ikr@iitb.ac.in (I. K. Rana), stutiborgohain@yahoo.com (S. Borgohain) http://www.global-sci.org/ata/ 214 c 2014 Global-Science Press