On an explicit formula for inverse of triangular matrices | ||
| Journal of the Egyptian Mathematical Society | ||
| Volume 23, Issue 2, 2015, Pages 297-302 PDF (433.68 K) | ||
| Document Type: Original Article | ||
| DOI: 10.1016/j.joems.2014.06.001 | ||
| Authors | ||
| Pinakadhar Baliarsingh* 1; Salila Dutta2 | ||
| 1Department of Mathematics, School of Applied Sciences, KIIT University, Bhubaneswar 751024, India | ||
| 2Department of Mathematics, Utkal University, Vanivihar, Bhubaneswar, India | ||
| Abstract | ||
| 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. | ||
| Keywords | ||
| Difference operators BLða½mÞ and BUða½mÞ; Cesa`ro mean operator; Riesz mean and generalized mean operator | ||
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