AN INTRODUCTION TO $\mathfrak{U}$-METRIC SPACE AND NON-LINEAR CONTRACTION WITH APPLICATION TO THE STABILITY OF FIXED POINT EQUATION

K. Roy, M. Saha, D. Dey

Abstract

In this paper, we introduce the notion of $U$-metric space of $n$-tuples which generalizes several known metric-type spaces.
We study topological properties of such newly constructed spaces and prove Cantor's intersection-like theorem.
Banach contraction principle theorem is proved in this space and we apply the theorem to obtain the stability of a fixed point equation.

Keywords: $\mathfrak{U}$-metric space; Cantor's intersection like theorem; fixed point; stability of fixed point equation.