On some properties of quasi-linear operator
Gai Gong-qi · Journal of Natural Science of Heilongjiang University · 2007
The definition of quasi-linearity operators is first given,and then the relations of homogeneity,the quasi-additivity and idempotence of operators are discussed.In certain condition it has proven equivalence between the quasi-linearity and quasi-additivity of operators,and has proven that the range of the quasi-linear operators is closed.Continuity of the quasi-linear operators is obtained in its range,and a generalized Banach lemma for the bounded Quasi-linear operator in Banach space is given.