MEIR-KEELER OPERATORS AND APPLICATIONS TO SURJECTIVITY THEOREMS

The first purpose of this paper is to prove that, in a Banach space X, a Meir-Keeler operator f (singlevalued or multivalued) is a norm-contraction. Then, using this result, we will give sufficient conditions assuring that the field 1(x)-f, generated by f, is surjective. In the first section of the paper, we will recall some basic notions and results. Then, the second and the third sections contain surjectivity theorems for singlevalued and, respectively, multivalued Meir-Keeler operators. In the last chapter we present an application for the previous results. Our results generalize some well-known theorems of this type for Banach/Nadler type contractions.