(p, p; r)-convexity preserving infinite matrices

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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 languageEnglish (US)
Pages (from-to)445-455
Number of pages11
JournalApplied Mathematics E - Notes
StatePublished - Jan 1 2019

All Science Journal Classification (ASJC) codes

  • Applied Mathematics


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