 
Summary: Journal of
Mathematical
Inequalities
Volume 2, Number 2 (2008), 163184
DYNAMIC DOUBLE INTEGRAL INEQUALITIES IN
TWO INDEPENDENT VARIABLES ON TIME SCALES
DOUGLAS R. ANDERSON
(communicated by A. Peterson)
Abstract. First, we establish some new nonlinear dynamic inequalities in two independent vari
ables of Pachpatte type, that might be useful tools in the study of qualitative properties of solutions
of certain classes of dynamic equations on time scales. These results extend recent inequalities
for difference equations to the general timescale setting. Then, after establishing a nabla Jensen's
inequality, we relate several inequalities of HilbertPachpatte type that extend and unify recent
continuous and discrete inequalities of this type.
1. Introduction
The unification and extension of differential equations, difference equations, q 
difference equations,and so on to the encompassing theory of dynamic equations on time
scales was first accomplished by Hilger in his Ph. D. thesis [10]. Since then, timescale
calculus has made steady inroads in explaining the interconnections that exist among the
various differential and difference theories, and in extending our understanding to a new,
