Results in Nonlinear Analysis

On certain fixed point theorems for F-contractions in 2-metric spaces and their application

Hemavathy K — 2025-01-17

This paper focuses on investigating F-contractions in 2-metric spaces and proving multiple fixed point theorems related to these contractions. Through the definition and analysis of F-contraction map-pings in the context of 2-metric spaces, the research sheds light on the existence and uniqueness of fixed points. The findings enhance the over-all comprehension of fixed point theory and its applications, providing useful resources for further exploration in mathematical analysis and associated areas.

Blow-up solutions of a system of nonlinear the Klein-Gordon-Fock Type wave equations

Gülesin Balaban Yavuzyılmaz — 2025-01-17

We consider the initial boundary value problem for a system of strongly damped wave equations with homogeneous Dirichlet boundary conditions and a nonlinear source term. By applying a modification of the concavity method, we demonstrate that the solutions blow up for $p<3$ with arbitrary positive initial data. Furthermore, we show that the global solvability of the problem for
$p\geq 3$.

Generalized cayley graphs and group structure: Insights from the direct products of P₂ and C₃

Ayat A. Neamah — 2025-01-17

This work introduces a generalization of Cayley graphs, denoted Caym(ψ, S), where ψ is a finite group and S is a non-empty subset of ψ. In this construction, vertices are represented by m-dimensional column vectors with entries in ψ, and adjacency is determined by a matrix-based condition involving the inverse elements and a matrix of elements from S. We focus on elucidating the structure and fundamental properties of Caym(ψ, S) when the classical Cayley graph Cay(ψ, S) corresponds to the direct products P2 × P2
and P2 × C2. Through rigorous analysis, we reveal distinct structural characteristics arising from these specific group structures and their associated generating sets. The generalized Cayley graph, denoted as Caym(ψ, S), is a graph where the vertex set consists of all column matrices Xm, with each matrix having elements from the set Ψ. Two vertices Xm and Ym are adjacent if and only if Ym
−1, the inverse of Ym, is a column matrix where each entry corresponds to the inverse of the associated element in Ψ. Our findings provide valuable insights into the interplay between algebraic properties of groups and the topological features of their generalized Cayley graph representations. This study contributes to a deeper understanding of generalized Cayley graphs and their potential
applications in diverse fields such as network theory, coding theory, and cryptography.

Derivation of Sawada-Kotera and Kaup-Kupershmidt equations KdV Flow Equations from Derivative Nonlinear Schrödinger Equation (DNLS)

Murat Koparan — 2025-01-17

The mathematical models of problems that arise in almost every branch of science are nonlinear equations of evolution (NLEE). In the past years, equations of formation have gained a significant place in applied mathematics. This study is about the multiple scales method, known as the perturbation method, for the derivative nonlinear Schrödinger (DNLS) equation. In this report, the multiple scales method was applied for the analysis of the derivative nonlinear Schrödinger (DNLS) equation. And (1 + 1) dimensional fifth-order nonlinear Korteweg-de Vries (fKdV) type equations were obtained. So, we have demonstrated the relationship between the KdV equations and the DNLS-type equation.

Qualitative and Numerical Analysis to a Time-Fractional Stefan Convection-Diffusive Model Using Riemann-Liouville and Caputo Operators

Habeeb Aal-Rkhais — 2025-01-17

The importance of the time-fractional Stefan problem(SP) comes from its wide physical applications. In this study, we assume an advective-diffusive flux to derive the model of the fractional SP for linear advection and diffusion forces depending on a realistic ice-melting problem. The rescaling technique is significant in estimating the self-similar solutions for the Stefan model. Also, we consider the interface function to satisfy the time fractional SP including boundary and Stefan conditions. The fractional derivative method, particularly Riemann-Liouville and Caputo derivatives, is used to find approximated solutions. The SP and other related phase transition problems typically have a constitutive relation between quantity, enthalpy, and temperature that requires thorough derivation based on physical grounds. Since physical understanding requires mathematical analysis, we provide analytical formulas for weak solutions to the SP because the classical analytical approaches break down in the case of the changing interface. On the other hand, the time-fractional diffusion-convection equation is considered to estimate an approximated numerical solution by applying the Sumudu decomposition method (SDM). The proposed method depends on applying the Sumudu transform of the Caputo fractional derivative operator and then using the fractional integral of Riemann-Liouville. These processes are useful in handling the nonlinear term with ease. It is discovered that the Sumudu approach is precise and quick. The MATLAB software carried out all the computations and graphics. To show that the suggested technique is valid and applicable, illustrative examples are provided.

Comparison between the performance efficiencies of reverse osmosis and nanofiltration membrane systems in removing heavy metal ions from industrial wastewater

Raid Raho Omran — 2025-01-08

Toxic contaminants that impact the health of humans and other animals include industrial wastewater, including cadmium, cobalt, chromium, and lead ions. To protect the environment, technologies such as “Reverse osmosis” (RO) and “Nanofiltration” (NF) membrane systems efficiently remove these ions from industrial effluent. Industrial wastewater samples were generated at room temperature and treated with both membrane systems in the laboratory. The samples contained Cd, Pb, Cr, and Co ions at concentrations ranging from 10 to 500 ppm, pressures ranging from 3 to 11 bar, and pH levels ranging from 4±0.2 to 7±0.2. Based on the findings, the RO system was able to remove Pb, Cd, Co, and Cr ions with efficiency of 98.55%, 97.97%, 97.308%, and 97.106%, respectively, when operated under the following conditions: pH = 6±0.2, pressure = 11 bar, pollutants concentrations = 500 ppm, time =
90 min at 25±2 °C. Operating parameters included a pH of 6±0.2, a pressure of 11 bar, a concentration of pollutants of 500 ppm, a duration of 90 minutes at 25±2 °C, and removal efficiencies of 96.37 percent for Pb, 95.44 percent for Cd, 94.478 percent for Co, and 93.965 percent for Cr in the (NF) system.

On the radial solutions of a p-laplacian equation involving a nonlinear gradient term and initial datum

Arij Bouzelmate — 2025-01-28

The present paper establishes the existence, uniqueness and asymptotic behavior of positive radial solutions to the following ordinary differential equation with a positive initial datum
\begin{align*}
(|v^{\prime }|^{p-2} v^{\prime})^{\prime}+\dfrac{N-1}{r}|v^{\prime }|^{p-2} v^{\prime} +rv^{\prime } + v =0 \quad \text{ for} \ r>0,
\end{align*}
where $p>2$ and $N>1$.
We start by providing a result on the existence of radial positive solutions using the shooting method and an associated energy function. Next, we derived crucial findings regarding the behavior of entire solutions near infinity. More precisely, we prove that the solutions behave like the function $l/r$, where $l$ is a positive constant.

Fixed point theorems of suzuki-type contractions in s-metric spaces with ternary relation and applications

M. V. R. Kameswari — 2025-02-03

In this paper we dene a new class of Suzuki-type contractions and prove some results on xed points in S-metric spaces with ternary relation. As an application of our results, we prove the existence of solutions for some classes of nonlinear matrix equations and provide a convergence analysis. Also, our results generalize recent results from the literature.

Using intelligent optimization algorithms, determine the quality of the nitrogenous base substituted for the MT-ND5 gene sequence

Marwan S. Jameel — 2025-01-30

This paper focuses on the application of intelligent optimization techniques in genetic engineering, using the MT-ND5 gene sequence as a case study to determine the specificity of nitrogenous base substitution. We used data from the NCBI database and analyzed it using smart optimization algorithms for the mathematical model of the objective function of the type of dynamic programming that comes from the hidden Markov chain to find the chance of getting a true sequence that is highest. We compared the results with the intelligent methods, demonstrating the effectiveness of these solutions in speeding up and enhancing the accuracy of the analysis through MATLAB simulations.

On the novelty of ”Contracting Perimeters of Triangles in Metric Space”

Erdal Karapınar — 2025-02-06

In this note, we research whether the newly introduced notion of ”contracting perimeters of triangles” in the context of metric spaces is equivalent to ”a variant” of Banach contraction in the setting of G-metric spaces. By using the fact that G-metric spaces are equivalent to quasi-metric spaces, we conclude that the fixed-point theorems via ”contracting perimeters of triangles” is equivalent to a fixed point of the same mapping in the context of quasi-metric spaces

Fixed point Theorems of Multivalued Mappings of Integral Type contraction in Cone Metric Space and its Applications

K. Dinesh — 2025-02-20

In this research, we use integral type contraction requirements to learning the existence of fixed points for multivalued mappings in the context of cone metric spaces. Cone metric spaces are a generalization of conventional metric spaces that provide a more comprehensive framework for solving challenging issues in fixed point theory by exchanging an ordered Banach space aimed at the real number set. Multivalued mappings pose special difficulties in locating fixed points since they provide each input several outputs. In order to tackle this, we present integral type contraction conditions, which offer a broadened contractive structure that encompasses a variety of non-linear behaviors. This study's main contribution is the construction of novel fixed point theorems over multivalued mappings given these integral type conditions of use, which broadens the application of previously published fixed point results.

Necessary and sufficient conditions for functions defined by binomial distribution to be in a general class of analytic functions

Tariq Al-Hawary — 2025-03-03

In this paper, a comprehensive class ΘΨ(El, E2, E3) of univalent functions is examined in light of the recent findings on binomial distribution. Additionally, we provide some requirements for the functions B(λ, γ, ς), B(λ, π, ς)b and the operator L(λ, γ, ς) defined by the binomial distribution to be in these subclasses. This study will motivate the authors to discover new sufficient requirements, not only for binomial distributions but also for numerous other special functions. Additionally, we summarize many previous studies.

A History of Contraction Principles

Sehie Park — 2025-03-06

Recently we obtained several extensions of the Banach contraction principle, which appears frequently in many literature. From our 2023 Metatheorem, we deduce Theorem H on the equivalent formulations of completeness of quasi-metric spaces. From Theorem H, we derive the Banach contraction principle, its extended form (Theorem Q), the Rus-Hicks-Rhoades contraction principle (Theorem P), and others. Consequently, our Theorem H contains wellknown theorems of Banach, Covitz-Nadler, Oettli-Thera, Rus-Hicks-Rhoades, and some others.

PRIME STRONG IDEALS OF S-SEMIGROUP

PRAKASH PADOOR — 2025-03-10

A seminearring is a generalization of the notion nearring in which the elements need not have an additive inverse. A S-semigroup is a generalization of the notion N-group in which the scalars are from seminearring. In this paper, we define various prime strong ideals of a S-semigroup and obtain the relationship among them. We also establish the connections between completely equiprime, equiprime and completely prime strong ideals of a S-semigroup. The obtained results are illustrated with the suitable examples. We also prove that every equiprime strong ideal of a S-semigroup is 3-prime strong ideal. In addition, we show that (P : Q)_S is strong ideal of a seminearring S and prove related results.

Enhancing Data Security by Apply a Novel Approach Utilizing Kashuri Fundo Transform and Linear Function Combinations

Nada Sabeeh Mohammed — 2025-03-10

In today's interconnected digital landscape, safeguarding sensitive data against cyber threats has emerged as our paramount challenge. To fortify defenses against intruders, continual enhancement of security measures is imperative, leveraging cutting-edge mathematical methodologies. This research presents a novel iterative cryptographic method based on the successive Kashuri Fundo Transform of a linear combination of functions and complemented by its inverse counterpart, specifically tailored for decryption purposes. Beginning with a comprehensive procedural framework, we substantiate our findings through empirical results. Moreover, we extend the applicability of this methodology through generalization and iterative refinement, thereby bolstering its resilience against potential breaches.

On the Fekete-Szegö inequality for analytic functions via Hohlov operator on leaf-like domains

Kavitha P — 2025-03-20

This study examines the Fekete-Szegö inequality in relation to the classes of holomorphic functions, particularly starlike and convex functions of complex order. We obtain significant inequality for star-like, bounded turning, and close-to-convex functions by using the Hohlov operator and taking leaf-like domains into account. These findings improve our comprehension of function behavior in complex analysis and geometric function theory by extending traditional findings to broader contexts. We also give tight constraints on the coefficients and study certain examples of the Gaussian Hypergeometric function.

On self-similar dendrites in Hilbert space

Klara Allabergenova — 2025-03-29

We consider the relation of the ramification order of self-similar dendrites in $\mathbb{R}^d$ and in Hilbert space and their Hausdorff dimension and measure.

A note on maximal regularity in relation with measure theory

Mustapha Achehboune — 2025-03-25

We present a synthetic method based on double approximation (multilevel approach) to state the maximal regularity of nonautonomous evolution equations, of non-autonomous evolution problems, mainly those driven by closed operators arising from sesquilinear forms, which enjoy some analytic properties. The infinite product of semigroups and elementary results, mainly some classical remarkable sets, in measure theory will play a central role in technical calculus.

Mathematical Modeling of Stress Induced Type 2 Diabetes and Atherosclerosis: Numerical Methods and Stability Analysis

Aytekin Enver — 2025-04-03

Chronic stress can dysregulate the body's adaptive stress responses, influencing immune, vascular, and metabolic functions, which are significant in cardiovascular disease risks. This cumulative effect of stress can heighten vulnerability to cardiovascular events, particularly in individuals with existing conditions like diabetes. Repeated stress responses may lead to inflammation, endothelial dysfunction, and plaque instability, thereby increasing the risk of atherosclerosis [1]. This article highlights the biochemical stressors with a focus on the mechanistic link towards vascular dysfunction associated with diabetes-mediated stress within a proatherogenic context. Type 2 diabetes causes a spectrum of systemic metabolic dysfunctions with the hallmark features of severe hyperglycemia and associated hyperinsulinemia that both augment oxidative stress and inflammatory responses in the vascular system. These effects are compounded by stress, which induces biochemical stress through the upregulation of reactive oxygen species (ROS) [2, 3, 4, 5]. We propose using mathematical modeling to shed light on how stress-induced changes that lead to increased ROS levels and deleterious metabolic pathways further promote plaque formation, contributing to the critical necessity of stress management in attenuating cardiovascular pathologies in diabetic patients. The study highlights the necessity to identify mechanisms of stress-diabetes interactions on atherosclerosis, which may allow new strategies for improving therapeutics.