 
Summary: TIMESCALE INTEGRAL INEQUALITIES
DOUGLAS R. ANDERSON
Abstract. Some recent and classical integral inequalities are extended to the general
timescale calculus, including the inequalities of Steensen, Iyengar, Cebysev, and Hermite
Hadamard.
IF Preliminaries on Time Scales
he unition nd extension of ontinuous lulusD disrete lulusD qElulusD nd inE
deed ritrry relEnumer lulus to timeEsle lulus ws rst omplished y rilger
in his hFhF thesis VF ine thenD timeEsle lulus hs mde stedy inrods in explining
the interonnetions tht exist mong the vrious lulusesD nd in extending our underE
stnding to newD more generl nd overrhing theoryF he purpose of this work is to
illustrte this new understnding y extending some ontinuous nd qElulus inequlities
nd some of their pplitionsD suh s those y teensenD rermiteErdmrdD syengrD
nd !gey!sevD to ritrry time slesF
he following denitions will serve s short primer on the timeEsle lulusY they
n e found in egrwl nd fohner ID etii nd quseinov QD nd fohner nd eterson
RF e time sle T is ny nonempty losed suset of RF ithin tht setD dene the jump
opertors ; X T 3 T y
@tA a supfs P T X s < tg nd @tA a inffs P T X s > tg;
where infY Xa supT nd supY Xa infTF he point t P T is leftEdenseD leftEstteredD
