On Some Generalized Number Theoretic Functions and Ighachane-Akkouchi Holder's Inequalities
Omprakash Atale *
Department of Mathematics, Khandesh College Education Society's Moolji Jaitha College, India.
*Author to whom correspondence should be addressed.
Abstract
Aims/ Objectives: Recently, it has been shown by Ighachane and Akkouchi [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 Ighachane and Akkouchi, Holder’s inequalities for the derived generalized functions are established.
Keywords: Number theoretic functions, Holder's inequalities, Nielsen's beta function, extended gamma function