Sentence examples for maximum minimum solution from inspiring English sources

Then, is solvable and it has a maximum (minimum) solution.

In addition, if f is upper (lower) -preserving with upper (lower) bound -closed values at all points in, then is solvable and it has a maximum (minimum) solution.

Along this line, Li and Ok [2] explore the order-preserving of generalized metric projection operator and study the existence of maximum (minimum) solutions to (operatorname{GVI}(C,Gamma)) on Banach lattices, where the considered mappings are required to have topped (bottomed) values.

The condition that has upper (lower) bound -closed values for some function, is not necessary for the problem to have a -maximum (minimum) solution to.

Example 3.7 leads us to consider some conditions on the mapping that are weaker than that in Theorem 3.1 which still guarantees the existence of a -maximum (minimum) solution to.

But, the existence of maximum or minimum solution will be failed.

The corresponding upper and lower bounds are defined using an estimate of the steepest gradient in terms of the maximum and minimum solution values at surrounding nodes.

In the end, we prove that (x^) and (y^) are maximum and minimum solutions for system (1.1).

Fluid-dynamic variables are searched with a probabilistic approach, meaning that for each variable the average, maximum and minimum solutions are calculated.

Now, we state and prove the main theorem of this paper below, which provides the existence of maximum and minimum solutions to general variational inequalities in Hilbert lattices.

In addition, the iterative schemes starting from some explicit initial values and converging to the exact maximum and minimum solutions are also constructed.