Search
17 articles for “Metric Spaces”
-
Comparative Evaluation of Fixed-Point Theorems Investigating Differences Among Conditions in Metric Spaces
Abstract: This paper provides a concise overview of metric spaces, their fundamental properties, and the idea of continuity as it pertains to these spaces, drawing parallels to uniform continuity and convergence. Also included is a review of previous research on metric space, its generalization, and practical outcomes from studies that utilized these spaces in various applications. We introduce a fixed point theorem for mixed monotone mappings in partially ordered metric spaces, …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 11, Issue 1, 2024 Read article
-
(𝛅,Ü ) Convex Structure on Partial B-Metric Space Concerning Quasi Contraction and Fixed-Point Results
Abstract: This work introduces the concept of (δ,Ü )– Convex Partial b-Metric Spaces using convex structure. Motivated by this approach, we demonstrated fixed point results and their uniqueness, as well as quasi contraction, and provided some supporting instances for the established results. Our findings expand prior fixed-point results to a novel concept (δ,Ü )– Convex Partial b-Metric Spaces. To support our theoretical findings, we provide several instances that exemplify the established …
Published in Recent Trends in Mathematics · Vol. 1, Issue 1, 2024 Read article
-
Equivalence Patterns in Racing: Examining Findings and Fixed-point Theorems in S-multiplicative Metric Space Integration
Abstract: The idea of equivalency patterns in racing is discussed in the abstract, along with research results and fixed-point theorems in relation to S-multiplicative metric space integration. Being a competitive activity, racing provides a rich environment for researching equivalency trends between rival enterprises. This article examines the dynamics of racing scenarios by exploring the mathematical structure of S-multiplicative metric spaces. The goal of this research is to identify fundamental properties and …
Published in Journal of Advanced Database Management & Systems · Vol. 11, Issue 2, 2024 · pp. 36–42 Read article
-
Intimate Mappings in Interval-Valued Fuzzy Metric Space: A Few Fixed-Point Findings
Abstract: The purpose of this study is to extend some previously established fixed point results for interval valued fuzzy metric space. For this objective, various contractive criteria with respect to an intimate mapping are applied. We employ intimate mapping in interval valued fuzzy metric space (IVFMS) to validate some well-known fixed point results. Our findings complement and generalize the recent findings of the common fixed point theorem for intimate mapping. The …
Published in Recent Trends in Mathematics · Vol. 1, Issue 1, 2024 · pp. 16–23 Read article
-
A Journey through Fixed Points and Non-expansive Mappings
Abstract: Fixed points in non-expansive mappings are elements that remain unchanged under the action of the mapping. Non-expansive mappings preserve or contract distances in a metric space. The rigorous proof of the Banach fixed-point theorem is presented at the outset of the paper, highlighting its fundamental significance. According to this theorem, every contraction mapping (a particular kind of non-expansive mapping that strictly reduces distances) has a single fixed point in a …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 11, Issue 1, 2024 Read article
-
Study of Proximity Points and Fixed Points
Abstract: This paper explores the concepts of proximity points and fixed points, which are fundamental in mathematical analysis and nonlinear functional analysis. Fixed-point theorems play a crucial role in optimization, game theory, differential equations, and dynamic systems. Proximity points, an extension of fixed points, provide a more generalized approach, allowing near-coincidence rather than exact identity. The study discusses classical fixed-point theorems, such as Banach’s contraction principle, Brouwer’s fixed-point theorem, and Schauder’s …
Published in Recent Trends in Mathematics · Vol. 1, Issue 2, 2024 · pp. 28–31 Read article
-
Extended Fixed Point Theorems in Menger PM-Type Spaces: Generalized Auxiliary Functions and Contractivity Conditions
Abstract: Background: Fixed point theory in probabilistic metric spaces, particularly Menger spaces, has been a subject of intensive research due to its applications in nonlinear analysis and mathematical modeling. Traditional approaches often impose restrictive constraints on the defining properties of Menger spaces and limit the class of auxiliary functions in contractivity conditions Methods: We extend recent fixed point theorems in Menger spaces by: (1) introducing the notion of Menger PM-type spaces …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 12, Issue 3, 2025 · pp. 1–6 Read article
-
A Study of Fixed-Point and Best Proximity Point
Abstract: Fixed-point theory plays a fundamental role in nonlinear analysis and has significant applications in optimization, differential equations, and applied mathematics. This study investigates the existence and properties of fixed points and best proximity points for various classes of mappings defined on metric and normed spaces. While fixed-point results guarantee the existence of a point that remains invariant under a given mapping, such points may not exist when the mapping is …
Published in Recent Trends in Mathematics · Vol. 3, Issue 1, 2026 · pp. 28–39 Read article
-
Exploration of Partial Order Structures in Menger Spaces Properties Characterizations and Applications
Abstract: Partial order structures play a crucial role in understanding the intricate relationships within mathematical spaces. In this paper, we delve into the realm of Menger spaces and investigate their properties through the lens of partial orders. Menger spaces, a generalization of metric spaces, possess unique characteristics that can be further elucidated by considering partial order structures. Through rigorous analysis, we explore various properties of partial order Menger spaces, including topological …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 11, Issue 3, 2024 · pp. 17–22 Read article
-
Expanding Hicks Contraction Theory, Multi-Valued Mappings in Generalized b-Menger Spaces
Abstract: This paper extends the Hicks contraction theory to multi-valued mappings within generalized b-Manger spaces, a class of metric-like structures that accommodate more flexible distance functions. By introducing new definitions, such as generalized admissibility conditions and weak compatibility in the multivalued sense, we provide a comprehensive analysis of how these contractions behave in broader topological and metric contexts. Our approach systematically generalizes classical contraction principles by relaxing conventional constraints, thereby broadening …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 12, Issue 1, 2025 · pp. 1–05 Read article
-
AI-Assisted Optimization of Supersonic Airfoil Shapes Using CFD Coupling
Abstract: This paper presents a novel framework for optimizing supersonic airfoil geometries through integrated artificial intelligence and computational fluid dynamics coupling. Traditional gradient-based optimization methods for high-speed aerodynamic shapes suffer from computational expense and convergence difficulties in non-convex design spaces. The proposed methodology employs a deep neural network surrogate model trained on high-fidelity Reynolds-Averaged Navier-Stokes solutions to approximate aerodynamic performance metrics across the design space. A hybrid particle swarm-genetic algorithm searches …
Published in Journal of Aerospace Engineering & Technology · Vol. 16, Issue 1, 2026 Read article
-
Firefly Algorithm–Based Optimization of Processing Parameters for Enhanced Performance of Polymer Composite Materials
Abstract: Polymer composite materials are extensively used in aerospace, automotive, and oil & gas applications due to their high strength-to-weight ratio and design flexibility. However, achieving optimal mechanical and thermal performance strongly depends on precise control of processing parameters such as curing temperature, energy consumption, and material utilization. Conventional trial-and-error approaches often lead to excessive energy usage, non-uniform curing, and sub-optimal composite properties. To address these challenges, this paper proposes an …
Published in Journal of Polymer & Composites · Vol. 14, Issue 1, 2026 · pp. 90–107 Read article
-
Rethinking Urban Design: Architectural Approaches to Walkability and Sprawl
Abstract: As cities stretch their concrete fingers across the landscape, architecture stands as both the problem and the solution. Like a master chess player, thoughtful architecture can reshape urban spaces, transforming car-centric sprawl into pedestrian-friendly havens. By crafting inviting streetscapes and mixed-use developments, architects weave a tapestry of walkable neighborhoods that pulse with life and connection. Streetscapes designed with wide sidewalks, pedestrian crossings, green spaces, and appropriate lighting further enhance the …
Published in International Journal of Urban Design and Development · Vol. 3, Issue 1, 2025 · pp. 25–33 Read article
-
A Novel Mathematical Exploration of Fractal Dynamics in Hyperbolic Spaces
Abstract: This research paper presents an original study on the behavior, generation, and properties of fractal structures within hyperbolic geometry. Unlike classical Euclidean fractals, hyperbolic fractals demonstrate accelerated boundary complexity and distinct scaling symmetries due to the curvature of the underlying space. The paper proposes new iterative models, analyzes geometric invariants, and explores potential applications in data visualization, network science, and theoretical physics. This research paper conducts an in-depth investigation into …
Published in Recent Trends in Mathematics · Vol. 3, Issue 1, 2026 · pp. 1–7 Read article
-
Implementation of website for Hind Enterprises Product: A Literature Review on Electronics perspectives, trends, and future directions
Abstract: The aim of Hind Enterprises’ product website is to develop a user friendly and informative online platform. That shows a diverse range of products. This website will serve as a comprehensive resource for manufacturing, business and individuals seeking information about machinery offering, specification and uses. The website will feature an intuitive and visually appealing design, ensuring seamless navigation for users. One primary goal of the project is to create a …
Published in International Journal of Solid State Innovations & Research · Vol. 2, Issue 2, 2024 · pp. 1–6 Read article
-
Review of Adaptive Cruise Control System
Abstract: New technologies are constantly being created in the modern era of the automotive industry to increase driver comfort and safety. The vehicle industry is focused on creating new designs that prioritize comfort and safety to overcome this problem. The technology which helps the automotive industry is the Adaptive Cruise Control system (ACC). The ACC system is an electronic device that assists drivers to keep a guarded distance from the upcoming …
Published in International Journal of Advanced Control and System Engineering · Vol. 1, Issue 1, 2023 · pp. 1–6 Read article
-
Automated Machine Learning System for Model Selection and Hyperparameter Optimization
Abstract: The proliferation of machine learning applications in various scientific and industrial domains has given rise to an urgent need for developing principled, automated techniques for optimal architecture selection and hyperparameter tuning for machine learning models without human expert intervention. In this paper, we introduce the Automated Machine Learning System for Model selection and hyperparameter Optimization (AMLSMO)—a state-of-the-art, all-encompassing AutoML system that combines the power of meta-learning-based warm-starting, Bayesian Optimization with …
Published in Recent Trends in Mathematics · Vol. 3, Issue 2, 2026 · pp. 15–23 Read article