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Highlights • A new class of fractal interpolants is established by a weighted average approach. • Sensitivity analysis of fractal interpolants with different weights is given. • Sensitivity analysis of fractal interpolants with different data set is given. • Stability analysis of fractal interpolants with variable parameters is given. • A discussion is given for random perturbations of interpolation points. Abstract Let { (t k , y k) ∈ R × Y : k = 0 , 1 , ... , N } be a given data set, where t 0 < t 1 < t 2 < ... < t N and Y is a real Banach space. For a given continuous interpolation function h on [ t 0 , t N ] and for each k = 1 , ... , N , the graph of h on subintervals [ t j (k, i) , t l (k, i) ], i = 1 , ... , n k , are transformed to the strip [ t k − 1 , t k ] × Y with endpoints (t k − 1 , y k − 1) and (t k , y k). Then a weighted average is applied to obtain the graph of a continuous function on [ t k − 1 , t k ]. A new continuous interpolation function on [ t 0 , t N ] can be established in this way and a fractal interpolant can be obtained by iteration. In this paper we introduce such a class of fractal interpolants and investigate some of their qualitative properties. [ABSTRACT FROM AUTHOR]

Fractal geometry is mainly based on the idea of self-similar forms. To be self-similar, a shape must able to be divided into parts that are smaller copies, which are more or less similar to the whole. There are different forms of self similarity in nature and mathematics. In this paper, some of the topological properties of super self similar sets are discussed. It is proved that in a complete metric space with two or more elements, the set of all non super self similar sets are dense in the set of all non-empty compact sub sets. It is also proved that the product of self similar sets are super self similar in product metric spaces and that the super self similarity is preserved under isometry. A characterization of super self similar sets using contracting sub self similarity is also presented. Some relevant counterexamples are provided. The concepts of exact super and sub self similarity are introduced and a necessary and sufficient condition for a set to be exact super self similar in terms of condensation iterated function systems (Condensation IFS’s) is obtained. A method to generate exact sub self similar sets using condensation IFS’s and the denseness of exact super self similar sets are also discussed. [ABSTRACT FROM AUTHOR]