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Báo cáo hóa học: " Research Article On Some New Sequence Spaces in 2-Normed Spaces Using Ideal Convergence and an Orlicz Function"

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 On Some New Sequence Spaces in 2-Normed Spaces Using Ideal Convergence and an Orlicz Function | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 482392 8 pages doi 10.1155 2010 482392 Research Article On Some New Sequence Spaces in 2-Normed Spaces Using Ideal Convergence and an Orlicz Function E. Savas Department of Mathematics Istanbul Ticaret University Uskudar 34672 Istanbul Turkey Correspondence should be addressed to E. Savas ekremsavas@yahoo.com Received 25 July 2010 Accepted 17 August 2010 Academic Editor Radu Precup Copyright 2010 E. Savas. 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 purpose of this paper is to introduce certain new sequence spaces using ideal convergence and an Orlicz function in 2-normed spaces and examine some of their properties. 1. Introduction The notion of ideal convergence was introduced first by Kostyrko et al. 1 as a generalization of statistical convergence which was further studied in topological spaces 2 . More applications of ideals can be seen in 3 4 . The concept of 2-normed space was initially introduced by Gahler 5 as an interesting nonlinear generalization of a normed linear space which was subsequently studied by many authors see 6 7 . Recently a lot of activities have started to study summability sequence spaces and related topics in these nonlinear spaces see 8-10 . Recall in 11 that an Orlicz function M 0 to 0 to is continuous convex 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. If convexity of Orlicz function M is replaced by M x y M x M y then this function is called Modulus function which was presented and discussed by Ruckle 13 and Maddox 14 . Note that if M is an Orlicz function then M Ax AM x for all A with 0 A 1. 2 Journal of Inequalities and Applications .