ABOUT A SUFFICIENT EXISTENCE CONDITION OF A SOLUTION TO THE EQUATION WITH NONMONOTONIC OPERATORS

摘要

In [1] one proved the theorem about the existence of a solution to the equation of type x = Fx, where F : E → E, E is a full structure, F is an isotonic operator. At the same time, the requirement of the isotone property of the operator essentially narrows the class of problems, to which this assertion can be applied. The mentioned theorem, which is known in the literature as the Birkhoff-Tarsky principle of the fixed point (e. g., [2], p. 26), was generalized in [3] for the case of the equation with the heterotonic operator.