Approximation of an Additive ϱ1,ϱ2-Random Operator Inequality

Abstract

We solve the additive ϱ1,ϱ2-random operator inequality ξtTω,u+v−Tω,u−Tω,v≥κMξtϱ1Tω,u+v+Tω,u−v−2Tω,u,ξtϱ22Tω,u+v/2−Tω,u−Tω,v, in which ϱ1,ϱ2∈ℂ are fixed and max2ϱ1,ϱ2<1. Finally, we get an approximation of the mentioned additive ϱ1,ϱ2-random operator inequality by direct technique.