Unconditional and Conditional Two-Power-Parameter Cyclic Inequalities

In this paper, we introduce unconditional and conditional cyclic inequalities involving two power parameters. By analyzing the non-negativity of difference functions, we generalize classical bounds for cyclic rational sums and establish new analytical results. We further determine the precise parameter ranges for which these global inequalities hold and discuss the conditions for the equality. Finally, several special cases of interest are highlighted.