Opial-type integral inequalities involving several higher order derivatives

AbstractIn this paper, we have established for the first time Opial-type integral inequalities involving a function and several higher order derivatives, which contain some known results of P. R. Beesack and K. M. Das (Pacific J. Math. 26, 1968, 215–232) and K. M. Das (Proc. Amer. Math. Soc. 22, 1969, 258–261). Some discrete Opial-type inequalities will also be studied. In the special cases they are similar to those of J. S. W. Wong (Canad. Math. Bull. 10, 1967, 115–118) and C. M. Lee (Canad. Math. Bull. 11, 1968, 73–77). Finally two examples are given to illustrate the application of our inequalities in differential equations