a generalized summability factor theorem for absolute summability and quasi power increasing sequences
نویسندگان
چکیده
the object of this paper is to establish a summability factor theorem for summabilitya, , k 1 k where a is the lower triangular matrix with non-negative entries satisfying certain conditions.
منابع مشابه
a summability factor theorem for absolute summability involving quasi power increasing sequences
we obtain sufficient conditions for the series σanλn to be absolutely summable of order k by atriangular matrix.
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Correspondence should be addressed to E. Savaş, [email protected] Received 23 June 2010; Revised 3 September 2010; Accepted 15 September 2010 Academic Editor: J. Szabados Copyright q 2010 E. Savaş. 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 ...
متن کاملA summability factor theorem for absolute summability involving almost increasing sequences
A triangle is a lower triangular matrix with all principal diagonal entriesbeing nonzero. Given an almost increasing sequence {Xn} and a sequence {λn} satisfying certain conditions, we obtain sufficient conditions for the series ∑ anλn to be absolutely summable of order k ≥ 1 by a triangle T . As a corollary we obtain the corresponding result when T is a weighted mean matrix. Theorem 1 of this ...
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In this paper we prove a general theorem on |A; δ|k -summability factors of infinite series under suitable conditions by using an almost increasing sequence, where A is a lower triangular matrix with non-negative entries. Also, we deduce a similar result for the weighted mean method. c © 2007 Elsevier Ltd. All rights reserved.
متن کاملA Recent Note on Quasi-Power Increasing Sequence for Generalized Absolute Summability
Quite recently, Savaş 1 obtained sufficient conditions for ∑ anλn to be summable |A, δ|k, k ≥ 1, 0 ≤ δ < 1/k. The purpose of this paper is to obtain the corresponding result for quasif-increasing sequence. Our result includes and moderates the conditions of his theorem with the special case μ 0. A sequence {λn} is said to be of bounded variation bv if ∑ n |Δλn| < ∞. Let bv0 bv ∩ c0, where c0 de...
متن کاملOn generalized absolute Cesàro summability
In this paper, a main theorem dealing with | C, 1 |k summability factors has been generalized under more weaker conditions for | C,α, β |k summability factors. This theorem also includes some new results. Mathematics Subject Classification 2000: 40D15, 40F05, 40G05, 40G99.
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عنوان ژورنال:
iranian journal of science and technology (sciences)ISSN 1028-6276
دوره 33
شماره 3 2009
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