# Purpose : the circle method is widely used to address problems of additive number theory. One of the modern tools involved is the mean value theorem (Vaughan, Wooley), which in some instance ...

We strictly formalized the three median value theorems of differentiation: Rolle's theorem, Lagrange's median value theorem, and Cauchy's median value theorem. This work lays a solid foundation for ...

Functions of single variable, limit, continuity and differentiability, mean value theorems, indeterminate forms; evaluation of definite and improper integrals; double and triple integrals; partial ...

Real analysis: inequalities, the continuum property, induction, sequences, functions and limits, continuity, contraction mappings and fixed points, differentiation, mean value theorems and Taylor's ...

The standard envelope theorems apply to choice sets with convex and topological structure, providing sufficient conditions for the value function to be differentiable in a parameter and characterizing ...

Melvyn S. Berger, Martin Schechter, Embedding Theorems and Quasi-Linear Elliptic Boundary Value Problems for Unbounded Domains, Transactions of the American Mathematical Society, Vol. 172 (Oct., 1972) ...