In the present article, we define difference operators BLða½mÞ and BUða½mÞ which represent a lower triangular and upper triangular infinite matrices, respectively. In fact, the operators
BLða½mÞ and BUða½mÞ are defined by ðBLða½mÞxÞk ¼ Pm
i¼0akiðiÞxki and ðBUða½mÞxÞk
¼ Pm
i¼0akþiðiÞxkþi for all k; m 2 N0 ¼ f0; 1; 2; 3; ...g, where a½m¼fað0Þ; að1Þ; ... aðmÞg, the set of
convergent sequences aðiÞ¼ðakðiÞÞk2N0
ð0 6 i 6 mÞ of real numbers. Indeed, under different limiting
conditions, both the operators unify most of the difference operators defined by various triangles
such as D;Dð1Þ
;Dm;DðmÞ
ðm 2 N0Þ;Da
;DðaÞ
ða 2 RÞ; Bðr;sÞ;Bðr;s;tÞ;Bðr~;s~;t
~; u~Þ, and many others.
Also, we derive an alternative method for finding the inverse of infinite matrices BLða½mÞ and
BUða½mÞ and as an application of it we implement this idea to obtain the inverse of triangular
matrices with finite support.