Discrete, Continuous, Delta, Nabla, and Diamond-Alpha Opial Inequalities

TL;DR: In this article, the authors proved diamond-alpha dynamic inequalities of Opial type with one and two weight functions on time scales, which contain as special cases improvements of results given in the literature, and these improvements are new even in the important discrete case.

Abstract: In this paper, we prove some new diamond-alpha dynamic inequalities of Opial type with one and with two weight functions on time scales. These results contain as special cases improvements of results given in the literature, and these improvements are new even in the important discrete case. Mathematics subject classification (2010): 39A10, 39A12, 26D15.

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M athematical
I nequalities
& A pplications
Volume 18, Number 3 (2015), 923–940 doi:10.7153/mia-18-69
DISCRETE, CONTINUOUS, DELTA, NABLA,
AND DIAMOND–ALPHA OPIAL INEQUALITIES
M
ARTIN J. BOHNER,RAMY R. MAHMOUD AND SAMIR H. SAKER
Abstract. In this paper, we prove some new diamond-alpha dynamic inequalities of Opial type
with one and with two weight functions on time scales. These results contain as special cases
improvements of results given in the literature, and these improvements are new even in the
important discrete case.
Mathematics subject classification (2010): 39A10, 39A12, 26D15.
Keywords and phrases: Time scales, diamond-alpha derivatives, Opial’s inequality.
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