We introduce a new class of generalized measures of relative deprivation. The class takes the form of a power mean of order p . A characteristic of the class is that depending on the value of the proximity-sensitive parameter p , the class is capable of accommodating both a decreasing weight (the case of p >1), and an increasing weight (the case of p~(0,1) ) accorded to given changes in the incomes of the individuals who are wealthier than the reference individual, depending on their proximity in the income distribution to the reference individual.