This paper deals with (p, p; r)-convexity of sequences. First, we give the necessary and suffi cient conditions for a non-negative infinite matrix to preserve (1, 1; 2)-convexity of sequences. Using this result, it is shown that the Borel matrix and the Ceśsaro matrix do not preserve (1, 1; 2)-convexity of sequences, thus proving that the theorem pertaining to Ceśsaro matrix given in  is incorrect. Furthermore, we prove that for any p ≠ 1, the Ceśsaro matrix does not preserve (p, p; 1)-convexity of sequences.
|Original language||English (US)|
|Number of pages||11|
|Journal||Applied Mathematics E - Notes|
|State||Published - Jan 1 2019|
All Science Journal Classification (ASJC) codes
- Applied Mathematics