Abstract
In a recent work (2016), the first author proved the fuzzy sum rule for the V-proximal subdifferential under some natural assumptions on an equivalent norm of the Banach spaces. In the present paper, we are going to prove that the class of Banach spaces satisfying the fuzzy sum rule is very large and contains all L-p spaces 1 < p<infinity as well as the sequence spaces l(p)(1 < p<infinity), the Sobolev spaces W-p,W-n (1 < p<infinity), and the Schatten trace ideals C-p(1 < p<infinity).