A note on Proinov contraction

Proinov contraction has appeared a several years ago as a new approach in the study of nonlinear contractions that unifies and extends several well-known classes of nonlinear contractions. What was not discussed is the relation of Proinov contraction and nonlinear contractions, especially Meir-Keeler contraction which also presents an important concept in Fixed point theory. The aim of this paper is to show that Proinov contraction is a Meir-Keeler contraction under some restrictions and that the obtained results under the scope of this contraction and its generalizations in this case are the direct consequence of the analogous results concerning Meir-Keeler contraction mappings. We will also present an example of a Meir-Keeler contraction that is not Proinov contraction and, additionally an example of Proinov contraction which is not a Boyd-Wong contraction, but is a Meir-Keeler contraction.