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Miskolc Mathematical Notes, vol.26, no.1, pp.335-365, 2025 (SCI-Expanded)
In this paper the classical nabla and delta Hardy-Copson type inequalities, which are derived for ζ?> 1, are complemented to the new case ζ < 0. These complements have exactly the same forms as the aforementioned classical inequalities except that the exponent ζ 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 ζ < 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.