An iterated function system that defines a fractal interpolation function, where ordinate
scaling is replaced by a nonlinear contraction, is investigated here. In such a manner, fractal …

The present note aims to establish the notion of non-stationary bivariate α-fractal functions
and discusses some of their approximation properties. We see that using a sequence of …

Following the seminal work of Barnsley on fractal interpolation, Navascués (2005) defined a
class of parametrized continuous functions called α-fractal functions. In this paper, we …

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In this study we provide several significant generalisations of Banach contraction principle
where the Lipschitz constant is substituted by real-valued control function that is a …

Most of the fractal functions studied so far run through numerical values. Usually they are
supported on sets of real numbers or in a complex field. This paper is devoted to the …

In this paper, we define inhomogeneous Graph-Directed (GD) iterated function systems and
show the existence of attractors for this new system. We also prove the existence of fractal …

In this article, we construct multivariate fractal interpolation functions for a given set of data
points and explore the existence of the α-fractal function corresponding to the multivariate …

Following the construction of fractal surfaces due to Ruan and Xu (Bulletin of the Australian
Mathematical Society 91: 435–446, 2015) and the theory of α-fractal functions due to …

In this article, we manifest the existence of a new class of α-fractal functions without endpoint
conditions in the space of continuous functions. Furthermore, we add the existence of the …