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.

MSC: 47H10, 54H25

Pages:  268$-$281     

Volume  73 ,  Issue  4 ,  2021