The terms 2-metric space and b-metric space are used interchangeably. The b2 -metric space introduced by Mustafa et al. (Z. Mustafa, V. Paraneh, J. Razaei, and Z. Kadulberg: b2 -metric spaces and some fixed point theorems, Fixed Point Theory and Applications 2014, 2014:144) is generalised. In this paper, we...