Inclusion relations among methods of four-dimensional summability compounded from given four-dimensional methods

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, and β nare sequences such that {α m} and {β n} are monotone increasing with αm′ ≥ αmand βn′ ≥ βnfor 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 r 1≤r ≤r 3and s ≤s 2≤s ≤⋯ constitute a double sequence of consistent family. Other implications and variations will also be presented