Related papers: Local fractal functions and function spaces
Within the new concept of a local iterated function system (local IFS), we consider a class of attractors of such IFSs, namely those that are graphs of functions. These new functions are called local fractal functions and they extend and…
Local iterated function systems are an important generalisation of the standard (global) iterated function systems (IFSs). For a particular class of mappings, their fixed points are the graphs of local fractal functions and these functions…
We define fractal interpolation on unbounded domains for a certain class of topological spaces and construct local fractal functions. In addition, we derive some properties of these local fractal functions, consider their tensor products,…
In this paper we present a systematic study of continuous local iterated function systems. We prove local iterated function systems admit compact attractors and, under a contractivity assumption, construct their code space and present an…
By appropriate choices of elements in the underlying iterated function system, methodology of fractal interpolation entitles one to associate a family of continuous self-referential functions with a prescribed real-valued continuous…
We introduce the novel concept of hypercomplex iterated function system (IFS) on the complete metric space $(\mathbb{A}_{n+1}^k,d)$ and define its hypercomplex attractor. Systems of hypercomplex function systems arising from hypercomplex…
In this article, we focus on the construction of multivariate fractal functions in Lebesgue spaces along with some properties of associated fractal operator. First, we give a detailed construction of the fractal functions belonging to…
We establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a…
The attractors of iterated function systems are usually obtained as the Hausdorff limit of any non-empty compact subset under iteration. In this note we show that an iterated function system on a boundedly compact metric space has compact,…
The concept of local fractional derivative was introduced in order to be able to study the local scaling behavior of functions. However it has turned out to be much more useful. It was found that simple equations involving these operators…
In these lecture notes we present connections between the theory of iterated function systems, in particular those attractors that are graphs of multivariate real-valued fractal functions, foldable figures and affine Weyl groups, and…
Let $G$ be a locally compact group and $1\leq p<\infty$. Based on some important earlier works, in this paper the concept of $L_p^T-$function is introduced. Then the structure of the space $L^{T}_p(G)$, which is consisting of all…
We introduce the novel concept of a non-stationary iterated function system by considering a countable sequence of distinct set-valued maps $\{\mathcal{F}_k\}_{k\in \mathbb{N}}$ where each $\mathcal{F}_k$ maps $\mathcal{H}(X)\to…
This paper presents a short introduction to local fractional complex analysis. The generalized local fractional complex integral formulas, Yang-Taylor series and local fractional Laurent's series of complex functions in complex fractal…
This paper presents the fractional trigonometric functions in complex-valued space and proposes a short outline of local fractional calculus of complex function in fractal spaces.
Fractal functions that produce smooth and non-smooth approximants constitute an advancement to classical nonrecursive methods of approximation. In both classical and fractal approximation methods emphasis is given for investigation of…
After proving the equivalence of the Bessel $K$-functional and the corresponding spherical modulus of smoothness we define fractional Bessel-Sobolev spaces. As an analog of the classical one the imbedding relation of fractional…
This paper studies smoothing properties of the local fractional maximal operator, which is defined in a proper subdomain of the Euclidean space. We prove new pointwise estimates for the weak gradient of the maximal function, which imply…
In this paper we define an internal binary operation between functions called in the text \emph{fractal convolution}, that applies a pair of mappings into a fractal function. This is done by means of a suitable Iterated Function System. We…
Theorems and explicit examples are used to show how transformations between self-similar sets (general sense) may be continuous almost everywhere with respect to stationary measures on the sets and may be used to carry well known flows and…