Generalization of istratescu's theorem on contractive mappings in metric spaces

In this paper we consider mappings T:XX of metric spaces, satisfying the condition: , where is some right semicontinuous function. We prove that if is a nondecreasing function, ()< for >0, –() as ,, then the map T has a fixed point and for any pointxX. Interesting examples are given.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol, 83, pp. 73–82, 1979.