Let ? be a positive finite Borel measure on the unit circle. The associated Dirichlet space D(?) consists of holomorphic functions disc whose derivatives are square integrable when weighted against Poisson integral ?. We give sufficient condition subset E circle which ensures that is uniqueness set for D(?). also some examples measures and sets

‎‎in this paper‎, ‎the existence and uniqueness of positive solutions for a class of nonlinear initial value problem for a finite fractional difference equation obtained by constructing the upper and lower control functions of nonlinear term without any monotone requirement‎ .‎the solutions of fractional difference equation are the size of tumor in model tumor growth described by the gompertz f...