Acta Mathematica Vietnamica

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Inclusion relations among methods of four-dimensional summability compounded from given four-dimensional methods
Richard F. Patterson

 

Abstract

The goals of this paper include the introduction of a new four-dimensional summability method construction by compounding a single four-dimensional method. The examination of this method begins with the characterization of its RH-regularity properties. In addition, the following inclusion and consistent theorems will be presented.

If {α m } , {β n } , {α m }, {β n } are sequences such that {α m } and {β n } are monotone increasing with α m αm and β n βn for all sufficiently large m and n and if the transformations B(α m ,β n )   and B(α m ,β n ) are factorable and RH-regular then B(α m ,β n )   includes B(α m ,β n ).

The RH-regular matrix transformations of the form B(r m ,s n ) for which r1r2r3≤⋯ and s1s2s3≤⋯ constitute a double sequence of consistent family. Other implications and variations will also be presented.

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