Jordan Journal of Mathematics and Statistics

Some Fixed Point Results in Complete b-Metric Spaces

Hakima Bouhadjera — 2025-10-13

The aims of this paper are threefold: the first is to prove the existence and uniqueness of common fixed points for two pairs of maps satisfying a new concept in a complete b-metric space, the second purpose is to produce two illustrative examples; on one hand, to show the applicability, validity and credibility of our results, and on the other hand, to show their superiority over several results, for instance the one’s of Roshan et al. [17], and the third and last objective is to apply one of our results to solve an integral equation.

Keywords: Complete b-metric spaces; occasionally weakly biased maps of type (A); unique common fixed points; integral equation.

2010 Mathematics Subject Classification. 47H10; 54H25

When does (P x n+1 +P x n−1 )/2 Equal a Pell-Lucas Number?

Djamel Bellaouar — 2025-10-13

In the present paper, we will find all solutions (m,n,x) for the equation P^x_n+1+P^x_n−1 = 2Q_m, where P_i is the i-th term of Pell sequence and Q_i is the i-th term of Pell-Lucas sequence.

Keywords: Exponential diophantine equations; Pell numbers; Pell-Lucas numbers; Linear forms in logarithms.

2020 Mathematics Subject Classification. 11B39; 11J86; 11D72

On the Maximum Likelihood Estimation for the Transmuted Extreme Value Distribution Parameters

MohammedRidha Kouider — 2025-10-13

Recently, researchers have been interested in the transmuted family of distributions via the quadratic rank transformation map, which was studied by Shaw and Buckley [21] (2009). Among the important distributions is the generalized extreme value distribution, due to its wide use in various fields. For this reason, we focus on estimating the parameters of the transmuted generalized extreme value (TGEV) distribution. Therefore, we develop transformed parameters of a generalized Pareto distribution (GPD) with a scale parameter and a shape parameter and approximate it to the transformed conditional distribution function to estimate the parameters of the TGEV via the maximum likelihood estimation (MLE). In a ddition, we present a numerical method for estimating the unknown parameters of the transmuted GPD starting from the MLE based on simple random sampling (SRS) and ranked set sampling (RSS). Finally, we present a simulation study using this practical method to better illustrate the findings of this investigation.

Keywords: Generalized Pareto distributions; Excesses over high thresholds; Maximum Likelihood Estimation; Ranked set sampling; Modified Bisection Algorithm.

2010 Mathematics Subject Classification. 62G32; 60G70

Estimation of Inverse Pareto Distribution through Different Loss Functions on Mortality Rate of COVID Data

Dr. Zaki Anwar — 2025-10-13

In this paper, the main objective is to estimate the parameter of inverse Pareto distribution based on lower record values. Hence, we consider the classical and Bayesian approaches to estimate the parameters of Inverse Pareto distribution (IPD), such as Maximum likelihood estimator(MLE), the general entropy loss function (GELF), the square error loss function (SELF), and the linear exponential loss function (LINEX). Further, simulation studies are performed to compare the different loss functions and confidence interval is also obtained for the given parameter. At last, covid data are used to compare the different results of estimations.

Keywords: Inverse Pareto distribution, Record values, Maximum Likelihood Estimates (MLE), SELF, LINEX, GELF, Bayesian estimation, Covid data.

2010 Mathematics Subject Classification. 62F10 ; 62F15

Bi-univalent Characteristics for a Particular Class of Bazilevič Functions Generated by Convolution using Balancing Polynomials

Gunasekar Saravanan — 2025-10-13

Bi-univalent functions, which are analytic and univalent in the open unit disk, have been a significant area of research in complex analysis due to their rich geometric properties. This study introduces a novel subclass of bi-univalent functions, called the Bazileviˇc functions class, which is created via the convolution of Balancing polynomials. We calculated the bounds for the Fekete-Szeg¨o inequality as well as the initial coefficients |a₂| and |a₃|. We have also included several relevant corollaries.

Keywords: Analytic function; Bi-Univalent function; Bazileviˇc functions; Convolution; Balancing polynomials.

2010 Mathematics Subject Classification. 30C45

Hopf Bifurcation Analysis in the Forest Pest System

Azad I. Amen — 2025-10-13

In this paper, we analyze dynamical behaviors of the non-even-aged forests affected by insect pest system. This system is described by a cubic system of three ordinary nonlinear differential equations with five real parameters. We confirm that the forest pest system displays local Hopf bifurcations under certain conditions. Moreover, we show that a Hopf bifurcation occurs at four equilibrium points for the system. Also, we obtain sufficient conditions for supercritical and subcritical bifurcations via the normal form theory.
More precisely, we show that the forest pest system admits limit cycles. Numerical examples are given to validate the theoretical analysis.

Keywords: Stability equilibrium point; Hopf bifurcation; limit cycles; Forest pest system.

2010 Mathematics Subject Classification. 34A34; 34C23; 34C25; 34D20

Dynamical Analysis of a Pest-Natural Enemy-Predator Model with Local Bifurcation Analysis

Pankaj Gulati — 2025-10-13

Crop protection is vital for agriculture-dependent economies, where pest infestations significantly threaten crop yields. This study develops a pest–natural enemy–predator model based on the Smith growth function, which more accurately represents ecological dynamics than the traditional logistic model. We analyze the system’s equilibrium stability and bifurcation behaviour with respect to the pest-capturing rate (ϒ), establishing the existence of a Hopf bifurcation. Numerical simulations support our analytical results, while MATCONT-based bifurcation analysis identifies limit points, Hopf bifurcations, and branch points, offering deeper insights into the system’s dynamic behaviour.

Keywords: Pest Population; Natural Enemy; Smith Model; Local Bifurcation; Branch point; limit point.

2010 Mathematics Subject Classification. 32G34; 34C23

Generalizations of p-Numerical Radii Inequalities for Operators

Raja’a Al-Naimi — 2025-10-13

Let T = [T_kj]ⁿ_k,j=1be an operator matrix, where T_kj is a Schatten p−class operator. Then ()..........................

Keywords: Inequality; Numerical radius; Operator; Norm; Schattenp-norm.

2010 Mathematics Subject Classification.15A18;15A42;47A63;47B07;47B15

Fuzzy Equivalence Relation and Fundamental Relation on Hyperalgebras

Mahsa Davodian — 2025-10-13

We introduce and study fuzzy hypercongruence relation on hyperalgebras as an extension of fuzzy congruence relation of algebras and present some important properties and isomorphism theorems. Then by applying the product concept for two fuzzy hypercongruence relations, it is determined that their product also constitutes a fuzzy hypercongruence relation. Finally, fundamental relation on the product of fuzzy subhyperalgebras are investigated.

Keywords: Hyperalgebra; Fuzzy equivalence relation; Fuzzy hypercongruence relation; Fuzzy factor hypercongruence; fundamental relation.

2010 Mathematics Subject Classification. 14L17; 08A72

Generalized Morphic Group Rings

Emad Abuosba — 2025-10-13

Let A be a commutative ring with identity, G be an abelian group, and consider the group ring AG. A ring A is called a generalized morphic ring (GM ring) if the annihilator of each element in A is principal. In this article, we showed that if AG is a GM ring, then so is A. The converse was proved to be false. We try to put some conditions on A or G to get the converse. Among many other results, we showed that if A is an Armendariz ring and G is a torsion free group, then AG is a GM ring if and only if A is. Moreover, if C_m denotes the multiplicative cyclic group of order m and Z the ring of integers modulo n, we justified that the ring Z_m is a GM ring if and only if, whenever p is a prime dividing gcd(n,m), then p² ∤ n. We also proved that for an integral domain D with char(D) = p, the group ring DC_p is a GM ring.

Keywords: Morphic ring; Generalized morphic ring; Morphic group ring; Generalized morphic group ring.

2020 Mathematics Subject Classification. 26A25; 26A35

On the Dirichlet-Hypergeometric Distribution on Symmetric Matrices

Mohamed Ben Farah — 2025-10-13

In this paper, we introduce an extension of the real Dirichlet-hypergeometric distribution to symmetric matrices, motivated by the need for structured matrix-valued distributions in multivariate analysis and random matrix theory. This matrix-variate generalization preserves the combinatorial and probabilistic foundations of the classical Dirichlet model while adapting them to the geometric and algebraic structure of symmetric matrices. We study distributional properties, including marginal and conditional distributions, the computation of moments, and derive the distribution of partial matrix sums. Furthermore, we introduce a class of related matrix distributions that naturally emerge in this framework. These results lay a foundation for further theoretical development and potential applications in areas requiring matrix-valued priors or structured random matrices.

Keywords: Dirichlet distribution; Gauss hypergeometric function; Liouville distribution; Transformation; symmetric matrices.

2010 Mathematics Subject Classification. 62E15; 60E05

Application of Neutrosophic Fuzzy Set for Efficient Placement of Health Centers for Marburg Virus

A. Sebasthiyar — 2025-10-13

The Ebola virus family has been accountable for the epidemic disease called Marburg virus disease, which has high fatality rates of up to 90%. Typically, health facilities deal with the afflicted persons while preventing the spread of infections. Therefore, temporary healthcare facilities are urged to treat the illness to stop the Marburg virus from spreading to other areas. The number of temporary health facilities that must be established in the impacted areas and the areas they serve are taken into consideration in this research. A savings heuristic is used to assign the temporary health centers to the afflicted regions, As for determining the weights of the affected sites, a single-valued neutrosophic fuzzy multi-criteria decision-making process is employed. The suggested neutrosophic fuzzy multi-criteria decision-making integrated saving heuristic approach is employed in conjunction with an efficient model. The results are thought to be advantageous for future multi-facility layout models.

Keywords: Marburg Virus; temporary health care centers; saving heuristic approach; neutrosophic fuzzy set.

2010 Mathematics Subject Classification. 26A25; 26A35

On a Mixture of the Lindley and Modified Lindley Distributions: Properties and Estimation

Christophe Chesneau — 2025-10-13

In this article, we investigate a novel three-parameter lifetime distribution constructed from a mixture of the original Lindley and modified Lindley distributions. The concept behind this construction is to combine the contrasting properties of these two well-known distributions to provide a new statistical modeling option for lifetime data analysis. In particular, it provides a natural alternative to the three-parameter, two-component mixture of the Lindley distribution, which has attracted attention in the recent statistical literature. We investigate its main properties from both a theoretical and practical point of view. The shapes of the corresponding probability density and hazard rate functions and the formulas for the moments, moment generating functions and characteristic functions are discussed. The distribution is then subjected to statistical analysis, considering it as a semi-parametric model. The maximum likelihood approach is used to estimate the parameters. In a simulation analysis, the numerical behavior of the bias and the mean square error of the obtained estimates are studied. The new model is tested on three data sets and the results show that it has a better fit behavior than its main competitor, the three-parameter two-component mixture of the Lindley model.

Keywords: Lindley distributions; maximum likelihood estimates; mixture distribution; modified Lindley distribution; moments.

2010 Mathematics Subject Classification. 26A25; 26A35

Nonlinear Noncanonical Second Order Neutral Difference Equations: Modified Oscillation Results

M. Madhan — 2025-10-13

In this paper, we derive some new oscillation criteria for the second-order nonlinear noncanonical neutral difference equation. The findings are novel and acquired through the transformation of the analyzed equation into canonical form, followed by the application of the summation averaging technique. Examples are provided to demonstrate the significance of the primary results.

Keywords: Oscillation; neutral difference equation; noncanonical; second-order.

2010 Mathematics Subject Classification. 39A10