SOME REMARKS ON RESULTS OF PEROV TYPE

In this paper, we consider, discuss, complement, improve and enrich some results of Perov type. By using the method of c-sequences we get much shorter proofs then ones in the papers with the Perov type theorems. Among other results we prove that one part of Perov type theorem (in the setting of generalized metric space) is equivalent to the classical Banach fixed point theorem. Furthermore, we give an example to show that the fixed point results of quasi-contraction of Perov type presented in the setting of normal and non-solid cone metric spaces are meaningful in the study of nonlinear integral equations.