Short communications

Existence of the fixed point in the case of evenly contractive monotonic operator

M. L. Katkov

South Ural State University

Abstract: The article proves the existence of the fixed point in the case of evenly contractive monotonic operator in the Banach $K$-space. It proved to be right that the iterations converge to the fixed point in the metric of the even convergence. Compactness of the invariant set and the total continuity of the operator are not assumed.

Keywords: positive operator; monotonic concave operator; heterotonic operator.

UDC: 517.988.52

Received: 28.05.2013