Research Article A Fixed Point Theorem Based on Miranda

Then, f (x) = 0 has a solution in Ω. For n = 1, Theorem 1.1 reduces to the well-known intermediate-value theorem. Miranda proved his theorem using the Brouwer fixed point theorem. Using the Brouwer degree of a mapping, Vrahatis gave another short proof of Theorem 1.1 (see [2]). Following this proof it is easy to see that Theorem 1.1 is also true, if L is dependent of i; that is, Ω can also be a rectangle and need not to be a cube. Even some Li can be zero. Very often, the theorem of Miranda is stated as in the following corollary (see also [3, 4]), which is not the theorem of Miranda in its original form, but a consequence of it.