Further on Opial type integral inequalities for superquadratic functions

The following inequality integral(c)(0) backslash psi(z)psi'(dz <= c/4 integral(c)(0)(psi'(z))(2)dz is well known in the literature as Opial's inequality [Z. Opial, Sur une inegalite, 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.