A NOTE ON GENERALIZED OPIAL TYPE INEQUALITIES

Authors

  • B. G. PACHPATTE Department of Mathematics and Statistics, Marathwada University, Aurangabad 431004, (Ma- harashtra), India.

DOI:

https://doi.org/10.5556/j.tkjm.24.1993.4494

Keywords:

integral inequality, Opial type inequality, convex function

Abstract

In the present note we establish some new inequalities involv- ing integrals of functions and their derivatives which in the special cases yield the well known Opial inequality and some of its generalizations.

References

E. K. Godunova and V. I. Levin, "On an inequality of Maroni (Russian)", Mat. Zametki 2 (1967), 221-224.

A. Kufner, 0 . John and S. Fucik, '1Function spaces", Noordhoff International Publishing Leyden, 1977.

D. S. Mitrinovic, "Analytic Inequalities", Springer-Verlag, Berlin, New York 1970.

C. Olech, "A simple proof of a certain result of z.Opial", Ann. Polon. Math. 8 (1960), 61-63.

Z. Opial, Sur une inegalite, Ann. Polon. Math. 8 (1960), 29-32.

B. G. Pachpatte, "On integral inequalities similar to Opial's inequality", Demonstratio Math. 22 (1989), 21-27.

G. I. Rozanova, "Integral inequalities with derivatives and with arbitrary convex functions (Russian)", Moskov. Gos. Ped. Jn,9t. Veen Zap. 460 (1972), 58-65.

G. S. Yang, "On a certain result of Z. Opial", Proc. Japan Aced. 42 ·(1966), 78-83.

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Published

1993-06-01

How to Cite

PACHPATTE, B. G. (1993). A NOTE ON GENERALIZED OPIAL TYPE INEQUALITIES. Tamkang Journal of Mathematics, 24(2), 229-235. https://doi.org/10.5556/j.tkjm.24.1993.4494

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Section

Papers