Points Of Mappings Research Articles

Inertial Halpern-type methods for variational inequality with application to medical image recovery

In this paper, we propose inertial Halpern-type algorithms involving a quasi-monotone operator for approximating solutions of variational inequality problems which are fixed points of quasi-nonexpansive mappings in reflexive Banach spaces. We use Bregman distance functions to enhance the efficiency of our algorithms and obtain strong convergence results, even in cases where the Lipschitz constant of the operator involved is unknown a priori. Furthermore, we illustrate the practical applicability of our methods through numerical experiments. Notably, our algorithms excel when compared to recent techniques in the literature. Of particular significance is their successful application in restoring computed tomography medical images that have been affected by motion blur and random noise. Our algorithms consistently outperform established state-of-the-art methods in all conducted experiments, showcasing their competitiveness and potential to advance variational inequality problem-solving, especially in the field of medical image recovery.

Double Inertial Krasnosel'skii-Mann-Type Method for Approximating Fixed Point of Nonexpansive Mappings

In this paper, we investigate a new method motivated by current advancements in general inertial algorithms. Specifically, we incorporate double inertial extrapolation terms into an iterative sequence, derived from Krasnosel'skii-Mann techniques. The weak convergence theorem for fixed points of nonexpansive mappings in real Hilbert spaces is established. The theoretical developments are rigorously proven, extending existing methods in literature. We also utilize our convergence analysis to solve real-world problems, such as convex minimization problems and zero finding for sums of monotone operators.

Some Common Fixed Point Results of Tower Mappings in (Pseudo)modular Metric Spaces

In this paper, we prove the existence and uniqueness of common fixed point of tower type contractive mappings in complete metric (pseudo)modular spaces involving the theoretic relation. However, the newly introduced contraction in this paper further characterize and includes in their full strength several existing results in metrical fixed point theory. Some nontrivial supportive examples were given to justify our result. Our results generalize, improve, and unify some existing results.

Integral Equations: New Solutions via Generalized Best Proximity Methods

This paper introduces the concept of proximal (α,F)-contractions in F-metric spaces. We establish novel results concerning the existence and uniqueness of best proximity points for such mappings. The validity of our findings is corroborated through a non-trivial example. Furthermore, we demonstrate the applicability of these results by proving the existence of solutions for Volterra integral equations related to population growth models. This approach not only extends best proximity theory, but also paves the way for further research in applied mathematics and beyond.

Common Fixed Point Results for Fuzzy F-Contractive Mappings in a Dislocated Metric Spaces With Application

This article presents a new approach to proving the existence and uniqueness of a common fixed point for fuzzy mappings that satisfy Ciric type F-contraction and Hardy-Roger type F-contraction in a complete dislocated metric space. These results are applied to multivalued mappings in dislocated metric spaces, and we have provided illustrative examples to demonstrate the power of our approach.

Research on a Matching Method for Vehicle-Borne Laser Point Cloud and Panoramic Images Based on Occlusion Removal

Vehicle-borne mobile mapping systems (MMSs) have been proven as an efficient means of photogrammetry and remote sensing, as they simultaneously acquire panoramic images, point clouds, and positional information along the collection route from a ground-based perspective. Obtaining accurate matching results between point clouds and images is a key issue in data application from vehicle-borne MMSs. Traditional matching methods, such as point cloud projection, depth map generation, and point cloud coloring, are significantly affected by the processing methods of point clouds and matching logic. In this study, we propose a method for generating matching relationships based on panoramic images, utilizing the raw point cloud map, a series of trajectory points, and the corresponding panoramic images acquired using a vehicle-borne MMS as input data. Through a point-cloud-processing workflow, irrelevant points in the point cloud map are removed, and the point cloud scenes corresponding to the trajectory points are extracted. A collinear model based on spherical projection is employed during the matching process to project the point cloud scenes to the panoramic images. An algorithm for vectorial angle selection is also designed to address filtering out the occluded point cloud projections during the matching process, generating a series of matching results between point clouds and panoramic images corresponding to the trajectory points. Experimental verification indicates that the method generates matching results with an average pixel error of approximately 2.82 pixels, and an average positional error of approximately 4 cm, thus demonstrating efficient processing. This method is suitable for the data fusion of panoramic images and point clouds acquired using vehicle-borne MMSs in road scenes, provides support for various algorithms based on visual features, and has promising applications in fields such as navigation, positioning, surveying, and mapping.

The Banach Fixed Point Theorem: selected topics from its hundred-year history

On June 24, 1920 Stefan Banach presented his doctoral dissertation titled O operacjach na zbiorach abstrakcyjnych i ich zastosowaniach do równañ całkowych (On operations on abstract sets and their applications to integral equations) to the Philosophy Faculty of Jan Kazimierz University in Lvov. He passed his PhD examinations in mathematics, physics and philosophy, and in January 1921 he became a doctor. A year later, he published the results of his doctorate in Fundamenta Mathematicae. Among them there was the theorem known today as the Banach Fixed Point Theorem or the Banach Contraction Principle. It is one of the most famous theorems in mathematics, one of many under the name of Banach. It concerns certain mappings (called contractions) of a complete metric space into itself and it gives the conditions sufficient for the existence and uniqueness of a fixed point of such mapping. In 2022 we had a centenary of publishing this theorem. In the paper, we want to present its most important modifications and generalizations, several contractive conditions, the converse theorems and some applications. It is not possible to provide complete information about what has been written during the last hundred years about the Banach Fixed Point Theorem and we are just trying to touch on some breakthrough moments in the development of the metric fixed point theory. The main purpose of this article is to organize the knowledge on this subject and to elaborate a broad bibliography which all interested persons can refer to.

Efficient iterative procedures for approximating fixed points of contractive-type mappings with applications

AbstractThis paper introduces and analyzes some new highly efficient iterative procedures for approximating fixed points of contractive-type mappings. The stability, data dependence, strong convergence, and performance of the proposed schemes are addressed. Numerical examples demonstrate that the newly introduced schemes produce approximations of great accuracy and comparable to other similar robust schemes appeared in the literature. Nevertheless, all the schemes developed here are more efficient than other robust schemes used for comparison.

Positioning the Quality Excellence Competitiveness of Integrated School Education Using the Multidimensional Scaling Model

This study was conducted by developing a performance analysis model of the competitiveness of Integrated Islamic Middle Schools (SMPIT). As a result of acquiring new students, SMPIT is experiencing increased student interest. The study aims to build a marketing strategy model based on competitive quality performance excellence and to determine the position of excellence of each SMPIT in Klaten City. The quantitative approach was used through a multivariate multidimensional scaling statistical test. The sampling technique used was purposive sampling, which included 112 respondents. The quantitative test of the model consists of the validity and reliability test of the instrument and the quantitative multidimensional scaling test of SMPIT competitiveness using the SPSS 21 program. This study produces attributes in the questionnaire including market orientation, program innovation, environmental adaptability and the influence of competitive advantage. The results of the quantitative test show that the instrument items are valid and reliable. SMPIT Ibnu Abbas and SMPIT Hidayah have the highest competitive advantage points in the competitiveness map of superior schools, both quantitative and qualitative, in Klaten Regency, namely in Quadrant I. The final stage of the research has formed a map of each SMPIT so that the competitiveness of superior Islamic high schools is created to welcome the era of demographic bonus and economic growth towards the golden generation of Indonesia in 2045. The novelty of this research is that it combines the concept of positioning the competitiveness of superior Islamic schools based on multidimensional scaling with the object of observation of secondary Islamic education. This study combines the idea of competitive advantage of the quality performance of Islamic educational institutions through the positioning of multidimensional scaling models.

Results on fixed points in b-metric space by altering distance functions

We discuss the existence of a fixed point for a self mapping and its uniqueness satisfying (ϕ˙,η˙)-generalized contractive condition including altering distance functions of rational terms in an ordered b-metric space. It is also discussed whether the two self-maps under the same contraction condition can be coincident and coupled coincident. The results are backed up by a dearth of numerical examples and application to nonlinear quadratic integral equation.

Three Existence Results in the Fixed Point Theory

In the present paper, we obtain three results on the existence of a fixed point for nonexpansive mappings. Two of them are generalizations of the result for F-contraction, while third one is a generalization of a recent result for set-valued contractions.

New L-fuzzy fixed point techniques for studying integral inclusions

The survey of the available literature shows that a lot of important invariant point problems of Banach and Heilpern types have been examined in both metric and quasimetric spaces. However, a handful of the existing results employed the recent approaches of interpolative contractions. Therefore, based on the new idea of interpolation techniques in fixed point theory, this article studies new notions of L-fuzzy contractions and investigates conditions for the existence of L-fuzzy fixed points for such mappings. On the fact that fixed points of point-to-point mappings satisfying interpolative-type contraction are not always unique, whence making the concepts more fitted for invariant point results of crisp set-valued maps, new multi-valued analogues of the key findings put forward in this work are derived. Comparative illustrations, which indicate the preeminence of the results presented herein, are constructed. From application viewpoint, one of the theorems so obtained is employed to introduce new solvability conditions of Fredholm-type integral inclusions.

Asymptotic Behavior of Generalized CR−iteration Algorithm and Application to Common Zeros of Accretive Operators

The purpose of this study is to provide a generalized CR−iteration algorithm for finding common fixed points (CFPs) for nonself quasi-nonexpansive mappings (QNEMs) in a uniformly convex Banach space. The suggested algorithm’s convergence analysis is analyzed in uniformly convex Banach spaces. Keywords: Fixed point, CR−iterative algorithm, nonself QNEMs.

Zeros of a Functional Associated with a Family of Search Functionals. Corollaries for Coincidence and Fixed Points of Mappings of Metric Spaces

Zeros of a Functional Associated with a Family of Search Functionals. Corollaries for Coincidence and Fixed Points of Mappings of Metric Spaces

Pure large kernel convolutional neural network transformer for medical image registration

Deformable medical image registration is a fundamental and critical task in medical image analysis. Recently, deep learning-based methods have rapidly developed and have shown impressive results in deformable image registration. However, existing approaches still suffer from limitations in registration accuracy or generalization performance. To address these challenges, in this paper, we propose a pure convolutional neural network module (CVTF) to implement hierarchical transformers and enhance the registration performance of medical images. CVTF has a larger convolutional kernel, providing a larger global effective receptive field, which can improve the network’s ability to capture long-range dependencies. In addition, we introduce the spatial interaction attention (SIA) module to compute the interrelationship between the target feature pixel points and all other points in the feature map. This helps to improve the semantic understanding of the model by emphasizing important features and suppressing irrelevant ones. Based on the proposed CVTF and SIA, we construct a novel registration framework named PCTNet. We applied PCTNet to generate displacement fields and register medical images, and we conducted extensive experiments and validation on two public datasets, OASIS and LPBA40. The experimental results demonstrate the effectiveness and generality of our method, showing significant improvements in registration accuracy and generalization performance compared to existing methods. Our code has been available at https://github.com/fz852/PCTNet.

Exploring Fixed Points and Common Fixed Points of Contractive Mappings in Complex-Valued Intuitionistic Fuzzy Metric Spaces

The current manuscript aims to introduce complex-valued intuitionisitic fuzzy metric spaces as a fresh perspective on complex-valued fuzzy metric spaces and intuitionistic fuzzy metric spaces. Existence together with distinctiveness of the fixed points within maps with diverse contractive criteria in this novel space are established. Additionally, our work yields a few common fixed-point findings for intuitionistic fuzzy Banach contraction on this newly introduced space. The outcomes presented in this study go beyond the existing literature, adding to the growing body of knowledge in this field. Our research outcomes are exemplified through examples that are included in this paper to help readers better grasp our findings. Our paper concludes with a discussion of how our findings can be applied to the problem of determining the presence of an exclusive solution for Fredholm integral equations.

Karyotype Description and Comparative Chromosomal Mapping of 5S rDNA in 42 Species.

This study was conducted to evaluate the 5S rDNA site number, position, and origin of signal pattern diversity in 42 plant species using fluorescence in situ hybridization. The species were selected based on the discovery of karyotype rearrangement, or because 5S rDNA had not yet been explored the species. The chromosome number varied from 14 to 160, and the chromosome length ranged from 0.63 to 6.88 μm, with 21 species having small chromosomes (<3 μm). The chromosome numbers of three species and the 5S rDNA loci of nineteen species are reported for the first time. Six 5S rDNA signal pattern types were identified. The 5S rDNA varied and was abundant in signal site numbers (2-18), positions (distal, proximal, outside of chromosome arms), and even in signal intensity. Variation in the numbers and locations of 5S rDNA was observed in 20 species, whereas an extensive stable number and location of 5S rDNA was found in 22 species. The potential origin of the signal pattern diversity was proposed and discussed. These data characterized the variability of 5S rDNA within the karyotypes of the 42 species that exhibited chromosomal rearrangements and provided anchor points for genetic physical maps.

Fixed points of continuous pseudocontractive mappings on convex, closed unbounded domains

The purpose in this article is to discuss under what conditions a continuous pseudocontractive mapping, in particular a nonexpansive map, has a fixed point when its domain is a closed, convex and unbounded subset of a Banach space. In fact, we will give a characterization of this property. The Halpern iterative algorithm for nonexpansive mappings is also investigated.

A proximal gradient method with double inertial steps for minimization problems involving demicontractive mappings

In this article, we present a novel proximal gradient method based on double inertial steps for solving fixed points of demicontractive mapping and minimization problems. We also establish a weak convergence theorem by applying this method. Additionally, we provide a numerical example related to a signal recovery problem.

Modified inertial subgradient extragradient with auxiliary parameters and parallel viscosity algorithm for minimization problem induced by bounded linear operator over common solution of fixed points of nonexpansive mappings and pseudomonotone equilibrium problems

Modified inertial subgradient extragradient with auxiliary parameters and parallel viscosity algorithm for minimization problem induced by bounded linear operator over common solution of fixed points of nonexpansive mappings and pseudomonotone equilibrium problems