Proximal Point Research Articles

Common best proximity point theorems in Hausdorff topological spaces

In the present paper, we have obtained common best proximity point theorems of nonself maps in Hausdorff topological space. Further, our results extend the results due to Gerald F. Jungck, thereby proving a generalized version of Kirk’s theorem (J. London Math. 1(1):107–111, 1969).

Clinical validity of the Japanese below-the-knee chronic total occlusion scoring system for the prediction of successful guidewire crossing

ObjectiveTo validate the Japanese below-the-knee (J-BTK) chronic total occlusion (CTO) score for the prediction of successful guidewire crossing (S-GC) in angiographic evaluation. MethodsA prospective, multicenter, nonrandomized study examined 751 consecutive BTK CTOs in 497 patients treated with endovascular therapy in 16 Japanese medical centers from April 2021 to March 2022. The cohort was classified into 2 groups: an S-GC group and a failed guidewire crossing group. ResultsThe J-BTK CTO score, which assigned one point to “Blunt type at the proximal entry point,” one point to “Calcification at the proximal entry point,” one point to “Reference vessel diameter <2.0 mm,” one point to “CTO length ≥200 mm,” and two points to “No outflow of the target vessel,” was used to categorize BTK CTOs into 4 grades with varying probabilities of S-GC: grade A (J-BTK CTO score of 0 and 1), grade B (score of 2 and 3), grade C (score of 4 and 5), and grade D (score of 6). Rates of S-GC in each grade (grades A, B, C, and D) were 97.5%, 89.1%, 62.5%, and 27.3%, respectively. The area under the receiver-operating characteristic curve for S-GC was 0.8304. Although the previous J-BTK CTO study enrolled only de novo lesions, both de novo and restenotic lesions were evaluated in this study. De novo lesions have a lower chance of S-GC (odds ratio: 0.24, 95% confidence interval: 0.09-0.67) in the multivariate analysis, and the area under the receiver-operating characteristic curve of the modified J-BTK CTO score, which additionally assigned two points to “De novo lesion,” was 0.846. The modified J-BTK CTO score showed an appropriate calibration (Hosmer-Lemeshow P = .957). ConclusionsThe J-BTK CTO score and the modified J-BTK CTO score predict the probability of an S-GC of BTK CTOs and stratify the difficulty of endovascular therapy for BTK CTOs in angiographic evaluation.

Best Proximity Point Theorems for Maia-Type Contraction Mappings

Best Proximity Point Theorems for Maia-Type Contraction Mappings

Proximal Point Method for Quasiconvex Functions in Riemannian Manifolds

Proximal Point Method for Quasiconvex Functions in Riemannian Manifolds

Proximal Point Algorithms with Inertial Extrapolation for Quasi-convex Pseudo-monotone Equilibrium Problems

Proximal Point Algorithms with Inertial Extrapolation for Quasi-convex Pseudo-monotone Equilibrium Problems

An Application of φ-Metric and Related Best Proximity Point Results Generalizing Wardowski’s Fixed Point Theorem

Abstract In this article, an application of φ-metric is given via a geometrical example to show how it can help to measure distance for non-planar surfaces where the classical metric becomes incapable. We also introduce the concept of best proximity point and proximal contraction for a class of mappings in a φ-metric space and prove a best proximity point theorem for such class of contraction mappings from which the famous “Wardowski’s fixed point theorem” can be deduced as a particular case. To support our theorem, we provide an example in which Wardowski’s metric fixed point theorem cannot be applied.

Asymptotic proximal point algorithm for wavefront sensorless adaptive optics.

Solving the distorted wavefront in wavefront sensorless adaptive optics (WFSL-AO) relies on excellent optimizers. Many local or global optimization algorithms have been applied to WFSL-AO; however, there is still a challenge to balance the effect and speed of correcting aberrations. To overcome this, a novel global optimization algorithm named asymptotic proximal point (APP) method is introduced into WFSL-AO in this Letter. We compare this algorithm with the various existing optimization algorithms in convergence speed and correction capability by performing numerical simulations. The results show that the APP method beats all competitors with a better correction effect and faster speed.

A new method for the construction of fractals via best proximity point theory

A new method for the construction of fractals via best proximity point theory

Recent Advances in Proximity Point Theory Applied to Fractional Differential Equations

Recent Advances in Proximity Point Theory Applied to Fractional Differential Equations

Comparative study of construction land development suitability assessment: Insights from multiple models and driving forces

Construction land development suitability (CLDS) assessment holds paramount importance in contemporary urban planning and management. Previous CLDS studies have faced challenges such as insufficient evaluation indicators, model complexity, and limited interpretability. To address these gaps, this study applies three simplistic yet mature models from the field of geological hazard assessment - Weight of Evidence (WOE), Information Value (IV), and Frequency Ratio (FR) - to evaluate the CLDS in Wuhan, China, and examine their feasibility. In parallel, a comparative analysis with the Patch-generating Land Use Simulation (PLUS) model was conducted. The WOE, IV, and FR models demonstrate a gradual decrease in CLDS from the city center and the Yangtze and Han rivers towards the periphery. Conversely, the PLUS model indicates the highest suitability around the city's development boundaries, followed by the city center, with suburbs displaying lower suitability. In terms of accuracy, the PLUS model's CARS module outperforms others, particularly for micro-level urban expansion simulations. The IV and WOE models follow closely, manifesting a preference for macro-level urban planning. Additionally, this study pinpoints key drivers influencing CLDS, notably population density, distance to social service Points of Interest (POI) and proximity to road networks. The cross-validation of the WOE, IV, and FR models underscores their reliability, with their straightforward principles positioning them as valuable tools in urban development planning. This comparative study validates the application of geological hazard models in urban contexts and diversifies CLDS assessment methodologies.

Fixed Point and Best Proximity Point Results in PIV-S-Metric Spaces

Fixed Point and Best Proximity Point Results in PIV-<i>S</i>-Metric Spaces

Antegrade anterior column acetabulum fracture fixation with cannulated compression headless screws-A biomechanical study on standardized osteoporotic artificial bone.

Due to the increase in life expectancy and high-energy traumas, anterior column acetabular fractures (ACFs) are also increasing. While open reduction and internal fixation (ORIF) is still the standard surgical procedure, minimally invasive, percutaneous fixation of osteoporotic acetabulum fractures (AF) are growing in popularity. The aim of this biomechanical study was to evaluate the biomechanical competence following antegrade fixation with a standard screw versus a cannulated compression headless screw. Eight anatomical osteoporotic composite pelvises were given an anterior column fracture. Two groups of eight specimens each (n = 8) for fixation with either a 6.5 mm cannulated compression headless screw in group Anterior Acetabulum Canulated Compression Headless Screw (AACCH), or with a 6.5 mm partially threaded cannulated screw in group Anterior Acetabulum Standard Screw (AASS) where compared. Each specimen was biomechanically loaded cyclically at a rate of 2 Hz with monotonically increasing compressive load until failure. Motions were assessed by means of optical motion tracking. Initial construct stiffness trended higher in group AACCH at 152.4 ± 23.1 N/mm compared to group AASS at 118.5 ± 34.3 N/mm, p = 0.051. Numbers of cycles and corresponding peak load at failure, were significantly higher in group AACCH at 6734 ± 1669 cycles and 873.4 ± 166.9 N versus group AASS at 4440 ± 2063 cycles and 644.0 ± 206.3 N, p = 0.041. Failure modes were breakout of the screws around the proximal entry point. From a biomechanical perspective, group AACCH was associated with superior biomechanical competence compared to standard partially threaded cannulated screws and could therefore be considered as valid alternative for fixation of anterior acetabulum fractures.

An inexact proximal point method with quasi-distance for quasi-convex multiobjective optimization

An inexact proximal point method with quasi-distance for quasi-convex multiobjective optimization

A systematic review and meta-analysis combining adolescent and adult data to evaluate weight loss and the effect of age following the laparoscopic sleeve gastrectomy.

Obesity is a grave concern within the United States, resulting in lost productivity, increased medical costs, and comorbidities with lifelong repercussions. The laparoscopic sleeve gastrectomy is a treatment option for obesity. The following meta-analysis sought to combine adolescent and adult literature to determine the overall effect of the sleeve gastrectomy on weight loss, to evaluate the effect of age at the time of surgery on weight loss, and to describe and explore variation in weight loss by sample characteristics. Overall weight loss was assessed at proximal and distal points, a dichotomous moderator variable analysis was conducted with subjects ≤21 years of age and >21 years of age, and a meta-regression assessing % male, % female, and baseline BMI was conducted to assess moderator variables. The laparoscopic sleeve gastrectomy was effective at facilitating weight loss with effect sizes varying from 0.916 to2.816. Age, biological sex, and baseline BMI were not found to have an impact on weight loss. The clinical consequences of prolonged obesity are evident and earlier intervention may be justified to counter the long-term effects caused by obesity related comorbidities. Standardized reporting of comorbidities and the effect of bariatric surgery on comorbid conditions is essential to allow further analysis.

Risk Assessment of Side Branch Compromise After Coronary Bifurcation Stenting - A Substudy of the 3D-OCT Bifurcation Registry.

Side branch (SB) occlusion during bifurcation stenting is a serious complication. This study aimed to predict SB compromise (SBC) using optical coherence tomography (OCT). Among the 168 patients who enrolled in the 3D-OCT Bifurcation Registry, 111 bifurcation lesions were analyzed to develop an OCT risk score for predicting SBC. SBC was defined as worsening of angiographic SB ostial stenosis (≥90%) immediately after stenting. On the basis of OCT before stenting, geometric parameters (SB diameter [SBd], length from proximal branching point to carina tip [BP-CT length], and distance of the polygon of confluence [dPOC]) and 3-dimensional bifurcation types (parallel or perpendicular) were evaluated. SBC occurred in 36 (32%) lesions. The parallel-type bifurcation was significantly more frequent in lesions with SBC. The receiver operating characteristic curve indicated SBd ≤1.77 mm (area under the curve [AUC]=0.73, sensitivity 64%, specificity 75%), BP-CT length ≤1.8 mm (AUC=0.83, sensitivity 86%, specificity 68%), and dPOC ≤3.96 mm (AUC=0.68, sensitivity 63%, specificity 69%) as the best cut-off values for predicting SBC. To create the OCT risk score, we assigned 1 point to each of these factors. As the score increased, the frequency of SBC increased significantly (Score 0, 0%; Score 1, 8.7%; Score 2, 28%; Score 3, 58%; Score 4, 85%; P<0.0001). Prediction of SBC using OCT is feasible with high probability.

A novel technique for the measurement of cervical length in non-pregnant women.

Cervical elongation is considered a risk factor for pelvic organ prolapse treatment failure in uterine preservation surgery. Consensus has not been reached regarding what is considered a normal cervical length, or how to measure it. Our primary aim was to test a new technique for measuring cervical length. We enrolled women undergoing hysterectomy, with or without pelvic organ prolapse (for all indications except cervical tumours/history of cervical operations). Their cervical lengths were measured both by ultrasound and anatomical measurement. The external length of the cervix was measured using Doppler location of the uterine artery near the cervical-uterine junction as the proximal point and compared to the ultrasound measurement of the cervical canal. The uterine specimen was used to record anatomical cervical measurements as well as uterine corpus length. Baseline characteristics such as age, body mass index and pelvic organ prolapse quantification were also collected. Twenty women were eligible for evaluation. We found the average anatomical cervical canal length was (ccAN) 33.95 mm (range ± 9.23) and by external measurement (ceAN) 36.80 mm (range ± 7.54). We found a significant, high-powered correlation between our ultrasound and anatomical measurements in both techniques, as well as between the two ultrasound techniques. We also found a negative correlation between cervical length and women's age (rp = -0.443, P = 0.05). Transvaginal ultrasound measurement of cervical length using the location of the uterine artery was found to have a strong correlation to the anatomical cervical length and can be used for the measurement of normal cervical length.

Best Proximity Point of Generalized θ-φ-Proximal Non-self Contractions

Best Proximity Point of Generalized θ-φ-Proximal Non-self Contractions

Linear Convergence of the Derivative-Free Proximal Bundle Method on Convex Nonsmooth Functions, with Application to the Derivative-Free VU\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal{VU}$\\end{document}-Algorithm

Proximal bundle methods are a class of optimisation algorithms that leverage the proximal operator to address nonsmoothness in the objective function efficiently. This study focuses on a derivative-free (DFO) proximal bundle method and one of its applications called the DFO VU\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal{VU}$\\end{document}-algorithm. These algorithms incorporate approximate proximal points as subprocedures in order to optimise convex nonsmooth functions based on approximated subdifferential information. Interestingly, the classical VU\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal{VU}$\\end{document}-algorithm, which operates on true subgradient values, achieves superlinear convergence. At each iteration, the algorithm divides the whole space into two: the smooth U\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal{U}$\\end{document}-space and the nonsmooth V\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal{V}$\\end{document}-space. It takes a Newton-like step on the U\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal{U}$\\end{document}-space and a proximal-point step on the V\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal{V}$\\end{document}-space, enabling it to handle both smooth and nonsmooth parts effectively and converge faster. In this work, we reveal the worst possible convergence rate for the DFO VU\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal{VU}$\\end{document}-method by showing the linear convergence of the DFO proximal bundle method. This will be done by presenting a suitable framework and using the subdifferential-based error bound on the distance to critical points.

Prediction of giant anomalous Nernst effect in Sm(Co,Ni)5

Sm-Co bulk alloys are well-known permanent magnets having large remanent magnetizations and coercive forces and are widely used in many industrial products. Recently, a large transverse thermoelectric conversion was observed for SmCo5 over a wide temperature range in the absence of magnetic fields. The large thermoelectric conductivity tensors (αxy) was also confirmed by the first-principles density functional theory (DFT) calculations. In this study, we predicted further enhancement of the αxy by including Ni in Co site of SmCo5. We showed that the αxy of Sm(Co1−xNix)5 increases with increasing the Ni ratio and takes the maximum value αxy = 11.3 A K−1 m−1 around x = 0.08 at 300 K, which is about 77% enhancement of αxy = 6.4 A K−1 m−1 in SmCo5. We clarified that the band proximity points near the nodal line of Sm(Co0.92Ni0.08)5 are the main contributing factor to the large Berry curvature, providing the steep slope of the energy dependence in the anomalous Hall conductivity around the Fermi energy.

Best Proximity Point Results via Simulation Function with Application to Fuzzy Fractional Differential Equations

In this study, we prove the existence and uniqueness of a best proximity point in the setting of non-Archimedean modular metric spaces via the concept of simulation functions. A non-Archimedean metric modular is shaped as a parameterized family of classical metrics; therefore, for each value of the parameter, the positivity, the symmetry, the triangle inequality, or the continuity is ensured. Also, we demonstrate how analogous theorems in modular metric spaces may be used to generate the best proximity point results in triangular fuzzy metric spaces. The utility of our findings is further demonstrated by certain examples, illustrated consequences, and an application to fuzzy fractional differential equations.