tailieunhanh - Báo cáo hóa học: " Research Article On Generalized Paranormed Statistically Convergent Sequence Spaces Defined by Orlicz Function ˘ Metin Basarir and Selma Altundag "

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 Generalized Paranormed Statistically Convergent Sequence Spaces Defined by Orlicz Function ˘ Metin Basarir and Selma Altundag | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 729045 13 pages doi 2009 729045 Research Article On Generalized Paranormed Statistically Convergent Sequence Spaces Defined by Orlicz Function Metin Basarir and Selma Altundag Department of Mathematics Faculty of Science and Arts Sakarya University 54187 Sakarya Turkey Correspondence should be addressed to Metin Basarir basarir@ Received 8 May 2009 Revised 3 August 2009 Accepted 26 August 2009 Recommended by Andrei Volodin We define generalized paranormed sequence spaces c ơ M p q s Cữ ơ M p q s m ơ M p q s and m0 ơ M p q s defined over a seminormed sequence space X q . We establish some inclusion relations between these spaces under some conditions. Copyright 2009 M. Baẹarir and S. Altundag. 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. 1. Introduction w X c X c0 X c X Cq X l CXf m X m0 X will represent the spaces of all convergent null statistically convergent statistically null bounded bounded statistically convergent and bounded statistically null X-valued sequence spaces throughout the paper where X q is a seminormed space seminormed by q. For X C the space of complex numbers these spaces represent the w c c0 c C0 l x m m0 which are the spaces of all convergent null statistically convergent statistically null bounded bounded statistically convergent and bounded statistically null sequences respectively. The zero sequence is denoted by 0 0 0 0 . where 0 is the zero element of X. The idea of statistical convergence was introduced by Fast 1 and studied by various authors see 2-4 . The notion depends on the density of subsets of the set N of natural numbers. A subset E of N is said to have density 0 E if 6 E lim 1 y xe K exists n--n n f f k 1 where XE is the characteristic function .