FURTHER ON OPIAL TYPE INTEGRAL INEQUALITIES FOR SUPERQUADRATIC FUNCTIONS

Abstract

The following inequality [Formula: see text] is well known in the literature as Opial’s inequality [Z. Opial, Sur une inégalité, Polon. Math. 8 (1960) 29–32], it had/has been studied extensively since its appearance. This paper investigates some of its generalizations in the prospect of generalized integral operators. From huge literature on this inequality, the results for superquadratic functions are considered and further analyzed for some integral operators. Several inequalities have been deduced for fractional integral operators by analyzing particular kernels.