Cantor’s Theorem in 2-Metric Spaces and its Applications to Fixed Point Problems

Abstract

2-metric space is an interesting nonlinear generalization of metric space which was conceived and studied in details by Gahler. In this paper, for the first time, we establish Cantor’s intersection theorem and Baire category theorem in 2-metric spaces. As a departure from normal practice we then apply Cantor’s theorem to establish some fixed point theorems in such spaces.