Sentence examples for be a concave operator from inspiring English sources

Let be a concave operator such that whenever and.

Since is a concave operator, it is easy to verify that is also a concave operator.

Since is a concave operator satisfying whenever and, we have that whenever and.

It is known that F is a concave operator with respect to w i j for elliptic u.

Let be the collection of all ordered pairs, where is a subspace of that contains and is a concave operator from to that extends and satisfies whenever and.

An operator is called a concave operator if is a nonempty convex subset of and if for all and all real number (2.7).

Then is called an concave operator.

So we need some properties of positive solutions for the operator equation Ax=lambda x, (1.1) where A is a generalized concave operator and (lambda>0) is an eigenvalue.

Let be replaced by a single-valued map in Corollary 3.3, then we have the following Hahn-Banach extension theorem in which a concave operator is dominated by a convex operator.

By Theorem 3.2, we can obtain the following new and interesting Hahn-Banach extension theorem in which a concave operator is dominated by a -convex set-valued map.

Since is a generalized concave operator, hence there exist real numbers, such that.