On some existence theorems for the solutions of a class of nonlinear operator equations

Theorems of M. A. Krasnosel'skii are generalized which concern fixed points of completely continuous operators which compress or expand a cone, and a topological principle for fixed points in the case of P-compact operators.Translated from Matematicheskie Zametki, Vol. 7, No. 2, pp. 229–237, February, 1970.The author expresses warm thanks to his advisor I. A. Bakhtin for constant help in this work.