In this paper, we show that, for any β∈[1, 2], a given strictly positive (or strictly negative) real-
valued continuous function on [0, 1] whose graph has the upper box dimension less than or …

This paper examines the integral transform of fractal interpolation functions with function
scaling factors. Initially, the integral transform of quadratic fractal interpolation function …

The goal of this article is to study the fractal surfaces and associated fractal operator on
Lebesgue spaces with respect to fractal measures. First, we show that fractal surfaces …

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 …

This study takes a broad approach to the fractal geometry problem and proposes an intrinsic
definition of the general box dimensions and the general Hausdorff and packing dimensions …

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In conventional ceramic–metal matrix composites, with the addition of the ceramic phase,
although it can significantly improve the performance of the material in one aspect, it tends to …

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 study the novel concept of non-stationary iterated function systems (IFSs)
introduced by Massopust in 2019. At first, using a sequence of different contractive …

In this article, we show that $\alpha $-fractal functions defined on Sierpi\'nski gasket
(denoted by $\triangle $) depend continuously on the parameters involved in the …