SOME WEIGHTED OPIAL-TYPE INEQUALITIES ON TIME SCALES

Abstract

Motivated essentially by several recent investigations which claimed to have generalized, improved and extended such classical inequalities as the well-known Opial's inequality, here we establish some general weighted Opial-type inequalities on time scales. We also provide counterexamples, corrections and modifications of the aforementioned recent claims by Wong et al. [Taiwanese J. Math., 12 (2008), 463-471].