Matrix Transformations of Summability and Absolute Summability Domains: The Case of Special Matrices
Ants Aasma, Hemen Dutta, P.N. Natarajan · 2017
This chapter is devoted to matrix transforms of summability and absolute summability domains of the Cesaro and Riesz methods. It focuses on the study of the necessary and sufficient conditions for M ε (cA, cB), M ε (csA, csB), M ε (bνA, cB), M ε (bνA, bνB), and considers the Mseq-consistency of matrix methods A and B on cA. The chapter explains the study of these problems in cases where A or both A and B are Cesaro or Riesz methods. In addition, for some special classes of matrices M, solving the above-mentioned problems, are presented. The chapter also considers the case if B = (R, qn) is also the Riesz method, given in the series-to-sequence form, and defined by the numbers qn. It describes some classes of matrices M, belonging to (cA, cB), for given matrix methods A and B.