Advanced topics in fractal interpolation theory

Fractal interpolation curves and surfaces are attractors of some iteration function systems associated with a given data set. Fractal interpolation provides a new insight to the approximation and modelling of experimental data. Fractal curves and fractal surfaces have attracted considerable attention due to their applications in areas such as Metallurgy Earth Sciences Surface Physics Chemistry and Medical Sciences. There are ?xed point theorems that can be used to the existence of attractors of iterated function systems and to the generation of fractal interpolation functions. In this book in order to give nonlinear fractal interpolation curves and surfaces with extensive practical applications we use Rakotch contractions and the Matkowski ?xed point theorem. In particular we extend our work and o?er a more comprehensive overview of our papers.