In this paper, we mainly make research on the approximation of continuous functions in the
view of the fractal structure based on previous studies. Initially, fractal dimensions and the …

In this paper, using two special types of rise-dimensional operators based on existing fractal
functions, we construct new fractal surfaces with any value of the Hausdorff and Box …

In this paper, we research on the dimension preserving monotonous approximation by using
fractal interpolation techniques. A constructive result of the approximating sequence of …

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 …

This article investigates fractal dimensions variation of fractal functions under certain
operations, which corroborates the conjecture raised in our previous work Yu and Liang …

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 …

Based on the previous studies, we make further research on how fractal dimensions of
graphs of fractal continuous functions under operations change and obtain a series of new …

The aim of this paper is to introduce and develop two novel classifications of enriched (q, θ)-
contractions on Banach spaces. The paper includes illustrative examples to demonstrate …

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 …

Rakotch contraction is a generalization of Banach contraction, which implies that in the case
of using Rakotch's fixed point theorem, we can model more objects than using Banach's …