On some generalized number theoretic functions and Ighachanea-Akkouchia Holder's inequalities

Recently, it has been shown by Ighachanea and Akkouchia \cite{0.1} that using binomial coefficients, one can derive some new refinements of Holder's inequalities. This inequalities then can be applied to a wide class of special functions such as the Nielsen's beta function and some extended gamma functions. In this paper, we have derived some generalizations of previously known number theoretic functions. Furthermore, based on the results of Ighachanea and Akkouchia, Holder's inequalities for the derived generalized functions are established.