Related papers: Digital Fixed Points, Approximate Fixed Points, an…
A generalized version of both rectangular metric spaces and rectangular quasi-metric spaces is known as rectangular quasi b-metric spaces (RQB-MS). In the current work, we define generalized $( \theta,\phi) $-contraction mappings and study…
Universal approximation theorems provide a mathematical explanation for the expressive power of neural networks. They assert that, under mild conditions on the activation function, feedforward neural networks are dense in broad function…
Function fitting/approximation plays a fundamental role in computer graphics and other engineering applications. While recent advances have explored neural networks to address this task, these methods often rely on architectures with many…
The universal approximation property of various machine learning models is currently only understood on a case-by-case basis, limiting the rapid development of new theoretically justified neural network architectures and blurring our…
The topology of digital images has been studied much in recent years, but no attempt has been made to exhaustively catalog the structure of binary images of small numbers of points. We produce enumerations of several classes of digital…
For functions defined via Dirichlet/generalized Dirichlet series in some half planes of the complex plane, we give a new simple elementary approach to obtain an Approximate Functional Equation(AFE for short) for the product of functions…
A topological neural network (TNN), which takes data from a Tychonoff topological space instead of the usual finite dimensional space, is introduced. As a consequence, a distributional neural network (DNN) that takes Borel measures as data…
We deal with values taken by various pseudopower functions at a singular cardinal that is not a fixed point of the aleph function.
Visually localizing an image, i.e., estimating its camera pose, requires building a scene representation that serves as a visual map. The representation we choose has direct consequences towards the practicability of our system. Even when…
Accurate 6-DoF pose estimation of objects is critical for robots to perform precise manipulation tasks. However, for dynamic object pose estimation, conventional camera-based approaches face several major challenges, such as motion blur,…
The universal approximation property (UAP) holds a fundamental position in deep learning, as it provides a theoretical foundation for the expressive power of neural networks. It is widely recognized that a composition of linear and…
In this paper, we first discussed multiplicative metric mapping by giving some topological properties of the relevant multiplicative metric space. As an interesting result of our discussions, we observed that the set of positive real…
Data coding as a building block of several image processing algorithms has been received great attention recently. Indeed, the importance of the locality assumption in coding approaches is studied in numerous works and several methods are…
We establish the first common fixed point theorem for commutative set-valued mappings. This may help to generalize common fixed point theorems in single-valued setting to those in set-valued. We also prove the existence of a fixed point in…
We present a novel, easy-to-use method based on the photon-mapping technique to simulate photometric images of moving targets. Realistic images can be created in two passes: photon tracing and image rendering. The nature of light sources,…
In this article, we give new results in the startpoint theory for quasi-pseudometric spaces. The results we present provide us with the existence of startpoint (endpoint, fixed point) for multi-valued maps defined on a bicomplete…
We explore the impact of aperture size and shape on automotive camera systems for deep-learning-based tasks like traffic sign recognition and light state detection. A method is proposed to simulate optical effects using the point spread…
We introduce Lipschitz continuous and $C^{1,1}$ geometric approximation and interpolation methods for sampled bounded uniformly continuous functions over compact sets and over complements of bounded open sets in $\mathbb{R}^n$ by using…
We call a function $f: X\to Y$ $P$-preserving if, for every subspace $A \subset X$ with property $P$, its image $f(A)$ also has property $P$. Of course, all continuous maps are both compactness- and connectedness-preserving and the natural…
In this paper, our aim is to obtain new fixed-disc results on metric spaces. To do this, we present a new approach using the set of simulation functions and some known fixed-point techniques. We do not need to have some strong conditions…