Jensen-Peari-Svrtan型不等式

Inequalities of Jensen-Peari-Svrtan Type

借助于优超理论,在适当的假设下建立了如下的Jensen-Peari-Svrtan型不等式,这里,A(.)表示算术平均.

By means of the theory of majorization,the following inequalities of Jensen-Pecaric-Svrtan type are established under proper hypothesesf（A（x））/f（A（φx））=fn,n（x）/fn,n（φx）≤（≥）…≤（≥）fk＋1,n（x）fk＋1,n（φx）≤（≥）fk,n（x）fk,n（φx）≤（≥）…≤（≥）f1,n（x）f1,n（φx）=A（f（x））A（f（φx））,where A（·） is the arithmetic mean andφ：[a,b]R,f：[a,maxt∈[a,b]{φ（t）}]R,fk,n（x）：=1（nk）∑1≤i1…ik≤nf（xi1＋xi2＋…＋xikk）,x∈[a,b]n.