Abstract：Sum-difference inequalities are the important tools to study existence， boundedness， uniqueness， continuous dependence of solutions on parameters and other qualitative properties of solutions of the difference equations. This paper studies a class of sixfold sum-difference inequalities in three independent variables， which include a nonconstant factor outside summarizing symbols and a nonconstant term outside summation term. The upper bounds of the unknown function in the sum-difference inequality is estimated explicitly using properties of difference operators， summing techniques， the techniques of change of variable， the method of amplification， the integral mean value theorem， and other analysis techniques， which generalized some known results. Finally an example is given to illustrate the results which is able to be used to study the qualitative properties of solutions of the difference equations with three independent variables.
陈立强,王五生. 一类三独立变量六重和差分不等式中未知函数的估计[J]. 华中师范大学学报(自然科学版), 2020, 54(3): 361-367.
CHEN Liqiang,WANG Wusheng. Estimation of unknown functions in a calss of sixfold sum-difference inequalities in three independent variables. journal1, 2020, 54(3): 361-367.