Mathematics

Concept extension for concave operator

M. L. Katkov

South Ural State University

Abstract: The class of monotone concave operators is considered by M. A. Krasnosel’sky. Significant development of this theory starts with V. I. Opoytsev’s definition of heterotone. In this paper we prove the convergence to the fixed point for a positive operator's iterations without hypothesis about monotonicity with a significant extension of the idea of concavity.

Keywords: positive operator, monotone operator, concave operator, heterotone operator.

UDC: 517.988.52

Received: 24.12.2013