@article{Shujat2025, 
author = {Faiza Shujat and Faarie Alharbi and Abu Zaid Ansari},
title = {Weak    (  p  ,  q  )-Jordan centralizer and derivation on rings and algebras},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {4},
pages = {8322-8330},
keywords = {weak (p, q)-Jordan derivations, weak (p, q)-Jordan centralizers, (semi) prime ring, right (left) (Jordan) centralizer, right (left) Jordan derivation},
url = {https://www.sciopen.com/article/10.3934/math.2025383},
doi = {10.3934/math.2025383},
abstract = {In the present paper, the authors discuss two new concepts that will be known as a weak    (  p  ,  q  )-Jordan centralizer and a weak    (  p  ,  q  )-Jordan derivation on an arbitrary ring    R and they prove that every weak    (  p  ,  q  )-Jordan derivation is a derivation on any prime ring    R. Furthermore, every weak    (  p  ,  q  )-Jordan centralizer is a centralizer on a semiprime ring    R. Later, they discuss the continuity of weak    (  p  ,  q  )-Jordan centralizer on a semisimple Banach algebra and prove that every weak    (  p  ,  q  ) -Jordan centralizer on a semisimple Banach algebra is a linear continuous operator. Moreover, these results are validated with actual examples.}
}