In addition, satisfies the subadditive condition.
In addition, satisfies the quasi-triangle inequality (2.3).
In addition, satisfy (2.2) for all and also satisfy (2.2) for all.
Then, if in addition, satisfies condition, the positive homoclinic solution of the equation (3.16).
When an agent's preferences in addition satisfy the independence condition and some other technical conditions, then they can be represented by an expected utility function (Harsanyi 1977b, ch. 4, Hernstein and Milnor 1953, Ramsey 1926, and Savage 1972).
Hence, we may assume that ({q_{k}:kgeq0}) satisfies conditions (3) and (4) and, in addition, satisfies the following condition: frac{Q_{n}}{q_{0}n}=o(1),quad text{as }nrightarrowinfty.
The infimum for Y in ((X,leq)), if it exists, is an element (zin X) which is a lower bound for Y and, in addition, satisfies (xleq z) provided that (xin X) is a lower bound for Y.
If (X subset Y) and (F : X rightarrow2^{Y}) is a mapping satisfying textit{for each } x in X textit{ there exists a } y in F x) textit{ such that } y preccurlyeq x. (4.3) Then for any (x_{0}in X), each maximal chain (A subset X ) containing (x_{0}) has a unique smallest element x, which in addition satisfies conditions (i), … , (iv) of Theorem 4.2 and is such that (x in F x)).
In addition, to satisfy the geometric conservation law (GCL) tensor identity under general moving meshes, a diagnostic approach is proposed based on the treatment of the GCL as an elliptic problem.
In addition, it satisfies Consistency Preservation, although not Rational Monotony.
