Complements of Nabla and Delta Hardy-Copson Type Inequalities and Their Applications

Abstract

In this paper the classical nabla and delta Hardy-Copson type inequalities, which are derived for zeta > 1, are complemented to the new case zeta < 0. These complements have exactly the same forms as the aforementioned classical inequalities except that the exponent zeta is not greater than one but it is less than zero. The obtained inequalities are not only novel but also unify the continuous and discrete cases for which the case zeta < 0 has not been considered so far either. Moreover one of the applications of Hardy-Copson type inequalities, which is to find nonoscillation criteria for the half linear differential/dynamic/difference equations, are presented by using complementary delta Hardy-Copson type inequalities.