The objective of this paper is to study the box-counting dimension of graphs of fractal
interpolation functions and harmonic functions on the Sierpiński gasket. Firstly, we give …

A general framework to construct fractal interpolation surfaces (FISs) on rectangular grids
was presented and bilinear FIS was deduced by Ruan and Xu (Bull Aust Math Soc 91 (3) …

Fractal interpolation function defined through suitable iterated function system provides a
method to perturb a function f∈ C (I) so as to yield a class of functions f α∈ C (I), where α is …

In this paper, we consider some generalization of the Banach contraction principle, namely
cyclic contraction and cyclic φ φ-contraction. For the application to the fractal, we develop …

The box dimension of the graph of non-affine α-fractal interpolation function f α with variable
scaling factors is estimated in the interval [0, 1]. Due to the non-affinity of f α, the behavior of …

The methodology of fractal sets generates new procedures for the analysis of functions
whose graphs have a complex geometric structure. In the present paper, a method for the …

In the framework of non-autonomous discrete dynamical systems in metric spaces, we
propose new equilibrium points, called quasi-fixed points, and prove that they play a role …

Fractal interpolation and approximation received a lot of attention in the last thirty years. The
main aim of the current article is to study a fractal trigonometric approximants which …

The box dimension of the graph of non-affine, continuous, nowhere differentiable function f α
which is a fractal analogue of a continuous function f corresponding to a certain iterated …

This article introduces fractal perturbation of rational functions via α-fractal operator and
investigates some approximation theoretic aspects of this new function class, namely, the …