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Recently, in [Electronic Transaction on Numerical Analysis, 41 (2014), pp.420-442] authors introduced a new class of rational cubic fractal interpolationfunctions with linear denominators via fractal perturbation of traditionalnonrecursive rational cubic splines and investigated their basic shapepreserving properties. The main goal of the current article is to embark onunivariate constrained fractal interpolation that is more general than what wasconsidered so far. To this end, we propose some strategies for selecting theparameters of the rational fractal spline so that the interpolating curves liestrictly above or below a prescribed linear or a quadratic spline function.Approximation property of the proposed rational cubic fractal spine is broachedby using the Peano kernel theorem as an interlude. The paper also provides anillustration of background theory, veined by examples.

Towards a More General Type of Univariate Constrained Interpolation With Fractal Splines