The complementary nabla Bennett-Leindler type inequalities

Abstract

We aim to find the complements of the Bennett-Leindler type inequalities in nabla time scale calculus by changing the exponent from $0<\zeta< 1$ to $\zeta>1.$ Different from the literature, the directions of the new inequalities, where $\zeta>1,$ are the same as that of the previous nabla Bennett-Leindler type inequalities obtained for $0<\zeta< 1$. By these settings, we not only complement existing nabla Bennett-Leindler type inequalities but also generalize them by involving more exponents. The dual results for the delta approach and the special cases for the discrete and continuous ones are obtained as well. Some of our results are novel even in the special cases.