MMN-3825
Complements of nabla and delta Hardy-Copson type inequalities and their applications
Zeynep Kayar; Billur Kaymakçalan;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.
Vol. 26 (2025), No. 1, pp. 335-365