Ralph Kenna's scaling relations in critical phenomena

In this note, we revisit the scaling relations among ``hatted critical exponents’’ which were first derived by Ralph Kenna, Des Johnston and Wolfhard Janke, and we propose an alternative derivation for some of them. For the scaling relation involving the behavior of the correlation function, we will propose an alternative form since we believe that the expression is erroneous in the work of Ralph and his collaborators.