### Abstract

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 [10] 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) |
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Pages (from-to) | 445-455 |

Number of pages | 11 |

Journal | Applied Mathematics E - Notes |

Volume | 19 |

State | Published - Jan 1 2019 |

### All Science Journal Classification (ASJC) codes

- Applied Mathematics

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## Cite this

Selvaraj, C. R., & Selvaraj, S. (2019). (p, p; r)-convexity preserving infinite matrices.

*Applied Mathematics E - Notes*,*19*, 445-455.