Vectorial inequalities for integral operators involving ratios of functions and convexity
Here we present vectorial integral inequalities for products of multivariate convex and increasing functions applied to vectors of ratios of functions. As applications we derive a wide range of vectorial fractional inequalities of Hardy type. They involve the left and right Riemann-Liouville fractional integrals and their generalizations, in particular the Hadamard fractional integrals. Also inequalities for Riemann-Liouville, Caputo, Canavati and their generalizations fractional derivatives. These application inequalities are of Lp type, p ≤ 1, and exponential type.
Discontinuity, Nonlinearity, and Complexity
Anastassiou, G. (2012). Vectorial inequalities for integral operators involving ratios of functions and convexity. Discontinuity, Nonlinearity, and Complexity, 1 (3), 279-304. https://doi.org/10.5890/DNC.2012.08.001