Sentence examples for a generalized concave from inspiring English sources

Then is called a generalized concave operator.

Since is a generalized concave operator, then there exists, such that (2.17).

Since is a generalized concave operator, we know that there exists, such that (2.12).

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

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.

We say an operator A is generalized concave if it satisfies the condition (ii) in Theorem 2.1; see [16].

The existence of a unique positive solution is proved only in the case where the cone P is normal and the operators A is generalized concave.

In this article, we first state and prove a new fixed point theorem for a class of generalized concave operators.

In this article we present a new fixed point theorem for a class of generalized concave operators and we establish some properties of positive solutions for the operator equation (Ax=lambda x).

In this paper, we generalize the concept of concave operators, give a concept of the generalized concave operators, and study the existence and uniqueness of fixed points for this class of operators by the iterative method.

In [19], by using a fixed point theorem of cone expansion and a fixed point theorem of generalized concave operators, the authors considered the existence, nonexistence, and uniqueness of convex monotone positive solutions of an elastic beam equation with a parameter.