Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Some New Double Sequence Spaces Defined by Orlicz Function in n-Normed Space | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2011 Article ID 592840 9 pages doi 2011 592840 Research Article Some New Double Sequence Spaces Defined by Orlicz Function in n-Normed Space Ekrem Savas Department of Mathematics Istanbul Commerce University Uskudar 34672 Istanbul Turkey Correspondence should be addressed to Ekrem Savas ekremsavas@ Received 1 January 2011 Accepted 17 February 2011 Academic Editor Alberto Cabada Copyright 2011 Ekrem Sava . This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. The aim of this paper is to introduce and study some new double sequence spaces with respect to an Orlicz function and also some properties of the resulting sequence spaces were examined. 1. Introduction We recall that the concept of a 2-normed space was first given in the works of Gahler 1 2 as an interesting nonlinear generalization of a normed linear space which was subsequently studied by many authors see 3 4 . Recently a lot of activities have started to study summability sequence spaces and related topics in these nonlinear spaces see . 59 . In particular Savas 10 combined Orlicz function and ideal convergence to define some sequence spaces using 2-norm. In this paper we introduce and study some new double-sequence spaces whose elements are form n-normed spaces using an Orlicz function which may be considered as an extension of various sequence spaces to n-normed spaces. We begin with recalling some notations and backgrounds. Recall in 11 that an Orlicz function M 0 to 0 to is continuous convex and nondecreasing function such that M 0 0 and M x 0 for x 0 and M x to as x to. Subsequently Orlicz function was used to define sequence spaces by Parashar and Choudhary 12 and others. An Orlicz function M can always be represented in the following integral form
