【摘要】 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.更多还原

【Abstract】 By means of the theory of majorization,the following inequalities of Jensen-Pecariˇc’-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.更多还原