(1) is a invariant quasimonotone mapping with respect to and on ; (2) and are affine in the first argument and skew; (3)for each and, there exist,, where, such that (4.29).
(1) is a pseudoinvex function with respect to and on ; (2) and are affine in the first argument and skew; (3)for any and, there exists such that (5.21).
(1) is a invariant pseudomonotone mapping with respect to and on ; (2) and are affine in the first argument and skew; (3)for each and, there exist,, where such that (5.22).
bit and sbit, unlike char and schar, allow the first argument to be an array of any rank.
Let be -Lipschitz continuous, let be a -Lipschitz continuous random operator, let be -Lipschitz continuous, and let be -strongly accretive with respect to and -Lipschitz continuous in the first argument and -Lipschitz continuous in the second argument, respectively.
Let be -strongly monotone and -Lipschitz continuous, and let be a -Lipschitz continuous random operator, and let be -strongly accretive with respect to and -Lipschitz continuous in the first argument, and -Lipschitz continuous in the second argument, -Lipschitz continuous in the third argument, respectively.
Let be -Lipschitz continuous, be a -Lipschitz continuous random operator, be -Lipschitz continuous and be -Lipschitz continuous in the first argument and -Lipschitz continuous in the second argument, respectively.
Let be a -strongly monotone with respect to the first argument and -Lipschitz mapping and be a -strongly monotone with respect to the second argument and -Lipschitz mapping.
Let be a -Lipschitz continuous random operator and be -Lipschitz continuous in the first argument, -Lipschitz continuous in the second argument and -Lipschitz continuous in the third argument, respectively.
The maps and are Carathéodory functions, which means that they are measurable in the first argument and continuous in the second one.
