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

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.