The Hausdorff–Pompeiu Distance in <i>Gn</i>-Menger Fractal Spaces

Abstract

This paper introduces a complete Gn-Menger space and defines the Hausdorff–Pompeiu distance in the space. Furthermore, we show a novel fixed-point theorem for Gn-Menger-θ-contractions in fractal spaces.

Keywords

• fixed point
• generalized contraction
• Hausdorff–Pompeiu distance
• iterated function system
• <i>Gn</i>-Menger fractal space