CATALAN MATRIX, BINOMIAL MATRIX, AND A NEWLY CONSTRUCTED ATALAN BINOMIAL INFINITE MATRIX METHOD WITH APPLICATION IN SUMMABILITY.

Abstract

Infinite matrices plays crucial roles in sequence and series spaces particularly in the summation of the divergent sequences and series. This paper explores the construction of a new matrix based summability method using the Catalan and the Binomial Matrices as the Base Matrix for its generation. The inverse of the Catalan and the Binomial Matrices were Obtained Under some imposed conditions and later on were characterized and applied to summability of some divergent sequences and series. The inverse of newly constructed infinite matrix was obtain and later on was characterized and applied to the summation of some the summation of some divergent sequences and series. Further, we presented every application alongside with its geometric view to clearly justify our results.