【摘要】 不等式M(1,x)+[M(2,x)]1 2M(1,x)·M(-1,x) n+n1 2n2是所谓的广义Malfatti型不等式.在较弱的条件下把它推广为更一般的形式.例如:a[M(λ,x)]1 λ+b[M(μ,x)]1 μM(λ,x)·M(μ,x)·M(1-λ-μ,x) an1 λ+bn1 μn3,这里M(β,x):=∑ni=1xβi,xi>0,β>1;a,b是两个正常数.所得结果包含最近的相关不等式,且建立不等式的方法是初等的,因仅仅利用了基本不等式.更多还原

【Abstract】 The inequalitiesM(1,x)+1/2M(1,x)·M(-1,x)n+n1/2n2 is the socalled generalized inequalities of Malfatti type. In this paper it is extended to the more general forms under the weaker conditions. For example,α1/λ+b1/μM(λ,x)·M(μ,x)·M(1-λ-μ,x)an1/λ+bn1/μn3, where M(β,x):=∑ni=1xβi,xi>0,β>1;a,b are two positive constants. The results include the recent related inequalities, since only some basic inequalities are used, the method of establishing the inequalities is elementary and short.更多还原