tailieunhanh - Báo cáo hóa học: " Research Article A Recent Note on Quasi-Power Increasing Sequence for Generalized Absolute Summability"

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 A Recent Note on Quasi-Power Increasing Sequence for Generalized Absolute Summability | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 675403 10 pages doi 2009 675403 Research Article A Recent Note on Quasi-Power Increasing Sequence for Generalized Absolute Summability E. Savas1 and H. Sevli2 1 Department of Mathematics Istanbul Ticaret University Uskudar 34672-Istanbul Turkey 2 Department of Mathematics Faculty of Arts Sciences Yuzttncu Yil University 65080-Van Turkey Correspondence should be addressed to E. Savas ekremsavas@ Received 15 May 2009 Accepted 30 July 2009 Recommended by Ramm Mohapatra We prove two theorems on A õf k 1 0 6 1 k summability factors for an infinite series by using quasi-power increasing sequences. We obtain sufficient conditions for y anXn to be summable I A 61k k 1 0 6 1 k by using quasi-f-increasing sequences. Copyright 2009 E. Savas and H. Sevli. 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 Quite recently Savas 1 obtained sufficient conditions for y anxn to be summable A 6 k k 1 0 6 1 k. The purpose of this paper is to obtain the corresponding result for quasi- -increasing sequence. Our result includes and moderates the conditions of his theorem with the special case p 0. A sequence 1 is said to be of bounded variation bù if yn I Al TO. Let bv0 bv n Co where Co denotes the set of all null sequences. The concept of absolute summability of order k 1 was defined by Flett 2 as follows. Let y an denote a series with partial sums sn and A a lower triangular matrix. Then y an is said to be absolutely A-summable of order k 1 written that y an is summable IA k k 1 if TO nk-1 Tn-1 - Tn k TO n 1 where n Tn 2 anvSv. 2 Journal of Inequalities and Applications In 3 Flett considered further extension of absolute summability in which he introduced a further parameter Ỗ. The series y an .