We first define weighted area balance function. Then we prove two identities for the integrable functions involving weighted area balance. Moreover, using these equalities, we obtain some inequalities for mappings of bounded variation and for Lipschitzian functions, respectively.
"Some inequalities for weighted area balance via functions of bounded variation." Rocky Mountain J. Math. 50 (2) 455 - 466, April 2020. https://doi.org/10.1216/rmj.2020.50.455