THE ANSWER TO AN OPEN QUESTION IN ℝm-b-METRIC SPACES AND APPLICATIONS TO INTEGRAL EQUATIONS

We give an affirmative answer to an open question in ℝm-b-metric spaces by using the subordinate property of the matrix norm to the ℓ∞-norm on ℝm. As applications, we get Perov’s fixed point theorem and Matkowski’s fixed point theorem in ℝm-b-metric spaces. We also show that the fixed point theorem in ℝm-b-metric spaces can be applied to prove the existence and uniqueness of the solution to an integral equation but fixed point theorems in metric spaces may not be.