On the box dimension of recurrent fractal interpolation functions defined with Matkowski contractions

Recurrent iterated function system (RIFS) represents an extension of the usual IFS method and allows the construction of more general sets, which do not have to exhibit the strict self similarity, and, in particular, the construction of recurrent fractal interpolation functions (RFIF). The box dimension of a graph of RFIF was first calculated by Barnsley et al. (Constr Approx 5:3-31, 1989) and, recently, was improved by Ruan et al. using the oscillation technique. In this paper, we construct and investigate a new class of RFIF defined with Matkowski contractions and we give an estimation of the upper bound of the box dimension of graphs of the RFIF.