CONVERSE ROGERS-H OLDER’S INEQUALITY ON TIME SCALES

TitleCONVERSE ROGERS-H OLDER’S INEQUALITY ON TIME SCALES
Publication TypeJournal Article
Year of Publication2006
AuthorsHong, C-H, Yeh, C-C
Secondary TitleCommunications in Applied Analysis
Volume10
Issue3
Start Page397
Pagination406
Date Published08/2006
Type of Workscientific: mathematics
ISSN1083–2564
AMS26D15, 26D20
Abstract

Converse Rogers-Holder’s inequalities are established on time scales by using elementary method.

URLhttp://www.acadsol.eu/en/articles/10/3/8.pdf
Short TitleConverse Rogers-H ̈older’s Inequality
Refereed DesignationRefereed
Full Text

REFERENCES

[1] M. Bohner and A. Peterson, Dynamic Equations on Time Scales, Birkh ̈auser, Boston-Basel-Berlin, 2001.
[2] J.B. Diaz, A.J. Goldman, and F.T. Metcalf, Equivalence of certain inequalities complementing those of  auchy-Schwarz and H ̈older, J. Res. NBS., 68B (1964), 147-149.
[3] V. Lakshmikantham, S. Sivasundaram, and B. Kaymakcalan, Dynamic Systems on Measure Chains, Kluwer Academic Publishers, Dordrecht-Boston-London, 1996
[4] X.H. Liu, On an inverse H ̈older’s inequality, Mathematics in Practice and Theorey, 20 (1990), 84-88.
[5] L. Maligranda, Why Holder’s inequality should be called Rogers’ inequality, Math. Inequ. Appl., 1 (1998), 69-83.
[6] A. W. Marshall and I. Olkin, Reversal of the Lyapunov, H ̈older and Minkowski inequalities and other extensions of the Kantorovich inequality, J. Math. Anal. Appl., 8 (1964), 503-514.
[7] D.S. Mitrinovc, Analytic Inequalities, Springer-Verlag, Berlin-Heidelberg-New York, 1970.
[8] B. Mond and J.E. Jeˇcari ́c, On converses of H ̈older and Beckenbach inequalities, J. Math. Anal. Appl., 196 (1995), 795-799,
[9] C.L. Wang, On development of inverses of the Cauahy and Holder inequalities, Siam Review, 21 (1979), 550-557.