In this paper, we deal with sequence spaces inclusion equations (SSIE), which are determined by an inclusion where each term is a sum or a sum of products of sets of the form a(T) and f(x)(T) where f maps U+ to itself, and (...), the sequence x is the unknown and T is a given triangle. Here, we determine the set of all sequences x with positive entries such that (…) and (…) where (...). We are led to study, among other things, the inclusion equations (…) and (…) where (…) is the operator of first differences defined by (…) for (…) with (…). The first (SSIE) leads to determine the set of all sequences x such that (…) and (…) implies (…). These results generalize some of the results given in [1].
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In [6] and [9], the concepts of [..]-core and statistical core of a bounded number sequence x have been introduced and also some inequalities which are ana-logues of Knopp's core theorem have been proved. In this paper, using the concept of [..]-summability introduced by Savas, we characterize the matrices of the classes (...) and determine necessary and sufficient conditions for a matrix B to satisfy [..].
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