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23 articles for “theorems”
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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
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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
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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
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Advance Fixed Point Theorems and Its Application to Ordinary and Fractional Differential Equations
Abstract: In the present research, advanced results on the fixed point theorem are applied to typical boundary value problems. Finding a differential equation's solution under certain boundary conditions is the goal of typical boundary value topics. The article appears to extend new fixed point results to a new context, likely involving fractional operators with unique kernels, notably the Caputo-type fractional operator. This extension involves applying the fixed point theorem to a …
Published in Recent Trends in Mathematics · Vol. 1, Issue 1, 2024 · pp. 1–15 Read article
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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
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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
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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
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Role of Prey Refuge in Predator-Prey Dynamics with Nonlinear Functional Responses: A Mathematical Approach
Abstract: The Beddington-DeAnglis and Holling type II functional response with prey refuge are used in this study to propose and assess a prey-predator system. This study looks at the ecological effects of prey refuge and how it affects predator-prey relationships, highlighting how functional responses influence population dynamics. The dynamical behavior of the model has been shown, which consist the existence of positivity, boundedness, local stability, and global stability. In addition, stability …
Published in Journal of Polymer & Composites · Vol. 13, Issue 3, 2025 · pp. 523–537 Read article
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Monitoring eddy current density fluctuation and power management in doped Al 2 O 3
Abstract: Al2O3 nanowire presents fascinating electrical properties which span from insulating (dielectric) to superconducting. A model is designed to describe the Phenomenon of eddy electric current and eddy current density fluctuation. Ohmic type theorem is developed using the modified Green – Kubo theorem. With little modification Green-Kubo theorem is incorporated to explain the relationship between eddy current density, electric field, and electric conductivity. Then factor contributing eddy current density fluctuations are …
Published in Nano Trends – A Journal of Nano Technology & Its Applications · Vol. 26, Issue 1, 2024 · pp. 35–45 Read article
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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
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Dynamics of Prime Gap Sets: An Algorithmic and Set-Theoretic Approach
Abstract: In this paper, we present a theorem and an efficient algorithm for computing all prime numbers up to a given integer X. Our theorem establishes a relationship between the primes up to X and those up to (X+1)2, providing a theoretical foundation for the algorithm. The proposed method improves upon the traditional Sieve of Eratosthenes by dynamically eliminating multiples of primes using only the remaining numbers in the set, thereby …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 12, Issue 3, 2025 · pp. 20–25 Read article
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The Effect of Rare Earth (RE) Metal Doping of Zno, On Magnetic and Optical Properties of Zno Crystals Structure
Abstract: The magnetic and optical properties of magnetic semiconductors relays on the crystal structure, type and amount of dopant ions, and particle size. Then, the effect of rare earth metal (Dy, Eu, and La) doping on crystal structures, magnetic properties and optical properties are seen. It is revealed that the optical band gap of ZnO decrease down from 3.37eV up on doping with RE metals. Then, the Hamiltonian of the system …
Published in International Journal of Crystalline Materials · Vol. 2, Issue 2, 2025 · pp. 28–40 Read article
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Analysis of Die Corner Gap Formation for Strain Hardening Materials in ECAP Through an Upper Bound Sensitivity Approach: A Comparative Study
Abstract: In recent work, using a proposed central composite factorial analysis, the upper-bound theorem's theoretical concept for the equal channel angular pressing process are used. The upper-bound theorem-based theoretical solutions consider Tresca friction conditions and varied fillet radii at the die channel junction. When using AA5083's uniaxial mechanical properties, isotropic nonlinear work hardening is assumed. The ratio of the cumulative effective plastic strain to the time generated by the deformation zones, …
Published in Trends in Machine design · Vol. 12, Issue 3, 2025 · pp. 1–22 Read article
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Harmonically Varying Moving Load on Time-Dependent Uniform Beam Resting on Pasternak Foundation
Abstract: In this paper, we investigated elastic beam whose properties does not varies with spatial coordinate but constant along the span L of the beam. The moving load considered in this work is harmonically varying moving load with non-classical boundary conditions, time dependent boundary conditions in particular. Also, considered in this work is two parameters foundation which are Winkler and Pasternak foundations. Closed form solutions in plotted form are obtained using …
Published in International Journal of Electro-Mechanics and Material Behaviour · Vol. 3, Issue 2, 2025 · pp. 38–47 Read article
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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
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An Adaptive Approach for Real-Time Embedded System Design, Analysis and Optimization
Abstract: Real-time embedded systems are critical components in various domains, such as automotive, aerospace, healthcare, and industrial automation. The design, analysis, and optimization of these systems are vital to ensure their reliable and efficient operation. In this paper, we propose an adaptive approach for real-time embedded systems that aims to address the challenges faced during the development process while maintaining high-quality results. Our approach leverages adaptive techniques to dynamically adjust the …
Published in International Journal of Solid State Innovations & Research · Vol. 1, Issue 1, 2023 · pp. 8–14 Read article
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A Comprehensive Study of ZnxFe2-xO3 Nanoparticles: Assessing Magnetic Properties for Medical Imaging (MI)
Abstract: Diluted magnetic ZnxFe2-xO3 nanoparticles are special semiconducting nanoparticles which are recognized for their magnetic properties. A theoretical examination of Zn-doped αFe2O3 nanostructures reveals a range of structural and property variations, offering insights into their potential applications and behavior at the nanoscale. In this regard, Heisenberg’s model and Weiss molecular filed theory is used to describe the magnetic properties of ZnxFe2-xO3 nanoparticles. These theorems inevitably enable to investigate the relationship between …
Published in Nano Trends – A Journal of Nano Technology & Its Applications · Vol. 26, Issue 2, 2024 · pp. 18–25 Read article
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Primality Testing: A Comprehensive Analysis of Methods and Time Complexity
Abstract: This paper examines various primality testing algorithms and analyzes their time complexity. The algorithms we examine include the trial division, which is straightforward but becomes inefficient with large numbers; Fermat’s little theorem which is a probabilistic method included in Monte Carlo type of randomized algorithm; the Solovay–Strassen, based on properties from number theory, particularly those related to Euler’s criterion and Jacobi symbols; and the Miller–Rabin Probabilistic Test, which balances efficiency …
Published in International Journal of Algorithms Design and Analysis Review · Vol. 2, Issue 2, 2024 · pp. 25–31 Read article
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Modelling Electronic Diode Networks with PSPICE Simulation
Abstract: The dual of Thevenin, Norton equivalent circuit is used in place of any circuit/network of linear sources and immittances at at a given frequency. Both Thevenin with Norton theorem is useful for analyses and modification of circuits, to study /obtain network’s steady state response and initial condition. Methods to represent different circuits with Thevenin/Norton impedances connected at desired nodes are given using Spice/Pspice. The Thevenin/Norton impedances connected are of other …
Published in International Journal of VLSI Circuit Design & Technology · Vol. 2, Issue 2, 2024 · pp. 17–37 Read article
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Investigation of bio-physical interaction between Nanoparticles, Colloids, and biomolecules: Pharmaco-medical application.
Abstract: Currently, research into magnetic nanoparticles has become Popular. The fundamental principle involving the physics of magnetic nanoparticles is its interaction with biomolecules such as hemoglobin, DNA, and RNA. In this research, the nature Vander walls interactions, electrostatic repulsion, thermal interactions, and magnetic interaction between nanoparticles and molecule is explored. The interaction parameters such as Zeta potentials between layer, magnetic moment density, and Gibbs energy can are discussed by using DLVO …
Published in Research & Reviews : Journal of Physics · Vol. 13, Issue 3, 2024 · pp. 6–17 Read article