TY - JOUR
T1 - (p, p; r)-convexity preserving infinite matrices
AU - Selvaraj, Chikkanna Ramalingam
AU - Selvaraj, Suguna
PY - 2019/1/1
Y1 - 2019/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85077356501&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85077356501&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:85077356501
SN - 1607-2510
VL - 19
SP - 445
EP - 455
JO - Applied Mathematics E - Notes
JF - Applied Mathematics E - Notes
ER -