Earthline Journal of Mathematical Sciences

Gegenbauer Polynomials for a Subfamily of Bi-univalent Functions

2025-04-02T15:10:14+00:00

We study a subfamily of bi-univalent and regular functions in the open unit disk subordinate to Gegenbauer polynomials. For functions in the defined subfamily, we derive initial coefficients bounds. Additionally, the Fekete-Szegö problem is handled for the elements of the defined subfamily. We also discuss relevant connections to previous findings and several fresh outcomes are shown to follow.

Power Series and Finite Element Methods for Solving Cahn-Hilliard Equation

2025-04-07T02:20:16+00:00

The Cahn-Hilliard equation is a nonlinear partial differential equation that describes spinodal decomposition, coarsening phenomena, and the dynamics of phase separation for ternary iron alloys. This article employs a power series technique and the finite element method to obtain analytical and numerical solutions of the Cahn-Hilliard equation, respectively. For the power series method, the nonlinear terms in the proposed problem are dealt with using the generalised Cauchy product of power series, which allows us to obtain an explicit recursion formula for the expansion function coefficient of the series solution. On the other hand, numerical solution to the Cahn-Hilliard equation is obtained using the finite element method that is based on the implicit time-stepping scheme and the sparse linear algebra technique. The obtained analytical and numerical solutions are compared with the exact solution to illustrate the accuracy and reliability of the proposed methods. The absolute errors obtained show that the proposed methods are accurate and reliable. Two and three dimensional graphs of the exact and approximate solutions are presented for comparison purposes.

Interpolative Berinde Weak Mapping Theorem on Partial Metric Spaces

2025-04-11T16:21:43+00:00

In this paper we introduce the notion of an interpolative Berinde weak operator in partial metric spaces. Additionally, we give an existence theorem for such operators in partial metric spaces. Finally, in support of the existence theorem, we provide an example.

New Iterative Methods and Sensitivity Analysis for Inverse Quasi Variational Inequalities

2025-04-14T17:00:49+00:00

Some classes of inverse quasi variational inequalities, which can be viewed as a novel important special case of quasi variational equalities, introduced in Noor [47] in 1988, are investigated. Using various techniques such as Wiener-Hopf equations, auxiliary principle, dynamical systems coupled with finite difference approach we suggest and analyzed a number of new and known numerical techniques for solving inverse quasi variational inequalities. Convergence analysis of these methods is investigated under suitable conditions. Sensitivity analysis is also investigated. One can obtain a number of new classes of inverse variational inequalities by interchanging the role of operators. Various special cases are discussed as applications of the main results. Several open problems are suggested for future research.

On Some Identities Related to Generalized Fibonacci and Lucas Numbers

2025-04-21T17:30:31+00:00

In this paper, we define some new matrices similar to the classical matrices introduced by Gould in [9]. We calculate the nth powers of the new matrices by diagonalizing them with the help of eigenvalues and eigenvectors. Thus, by making use of Binomial expansions, we obtain new identities containing generalized Fibonacci and Lucas numbers. These new results inform us about the relationships between matrix algebra and sequence theory, especially in the context of generalized Fibonacci and Lucas sequences.

Some Results for Third-Order Differential Subordination and Superordination Involving the Fractional Derivative and Differential Operator

2025-04-25T16:45:26+00:00

In the present paper, we define a certain suitable classes of admissible functions in the open unit disk associated with fractional derivative and differential operator. We derive some third-order subordination and superordination results for these classes. These results are applied to obtain third-order differential sandwich results. In addition, we indicate certain special cases and consequences for our results.

Second Derivative Mono-Implicit Runge-Kutta Methods

2025-05-01T16:52:30+00:00

Mono-implicit Runge-Kutta (MIRK) methods are Runge-Kutta methods having its stages depending on its output. In this paper, we develop a family of second derivative mono-implicit Runge-Kutta (SDMIRK) methods for the numerical solution of stiff initial value problems (IVPs) in ordinary differential equations (ODEs). The SDMIRK methods are extension of the MIRK having first and second derivative terms. The general order conditions for the stages and output methods are presented. The SDMIRK methods for stages s = 3 and s = 4 derived were found to be A-stable, while methods for s = 5 and s = 6 are A(α)-stable. Implementation procedures and numerical experiment are discussed herein. Results obtained by the SDMIRK method are favourable than the results of second derivative backward difference formular (SDBDF) and second derivative linear multistep method (SDLMM).

On Generalized co-Narayana Numbers

2025-05-02T16:47:17+00:00

In this paper, we introduce and investigate a new third order recurrence sequence so called generalized co-Narayana sequence and its two special subsequences which are related to generalized Narayana numbers
and its two subsequences. There are close interrelations between recurrence equations of and roots of characteristic equations of generalized Narayana and generalized co-Narayana numbers. We present Binet's formulas, generating functions, some identities, Simson's formulas, recurrence properties, sum formulas and matrices related with these sequences.

A Certain Class of Function Analytic and Subordinate to the Modified Sigmoid Function

2025-05-06T16:50:53+00:00

A certain class of functions, analytic and subordinate to the modified sigmoid function, is defined. Coefficient inequalities, Toeplitz, distortion, and Fekete-Szegö problems of this class were investigated. It was observed that the results obtained provide extensions to many known results in geometric function theory. Special cases of the results were equally highlighted.

Mathematical Analysis of a Tuberculosis-Schistosomiasis Co-infection Model with Vaccination and Treatment

2025-05-15T02:32:21+00:00

We present a mathematical model, that is deterministic, for investigating the impact of schistosomiasis infection on the immunogenicity of the BCG vaccine affects the use of vaccination as a measure of control against TB infection at population level in Nigeria. The presence of the backward bifurcation phenomenon was established from the analysis of the model, and it was discovered that the following parameters were responsible the adjustment parameter for comparative contagiousness of individuals re-contaminated with TB ($\Theta_{RT}$), the rate of therapy for schistosomiasis-only infected persons ($\zeta_S$), the impact of schistosomiasis on the BCG protection against TB ($\zeta_{TS}$), BCG vaccine waning ($\theta_V$), the BCG vaccine efficacy ($\epsilon_1$), the treatment rate for TB ($\zeta_T$), the comparative rates by which individuals having dormant schistosomiasis ($\eta_1$) cum virulent schistosomiasis ($\eta_2$) are tainted with TB, correspondingly, the depreciated rate of contamination with schistosomiasis ($\psi$), the regulation parameter for comparative infectiousness of persons possessing virulent TB cum dormant schistosomiasis ($\Pi_1$), the treatment rate for TB for co-infected persons ($\zeta_{T1}$), the progression rate from contagious TB/unprotected from schistosomiasis to contagious TB/contagious schistosomiasis ($\sigma$), and the rate of advancement from unprotected against the two infirmities TB/schistosomiasis to unprotected against TB/infectious schistosomiasis ($\alpha_2$). The disease-free equilibrium was found to be globally asymptotically stable when the parameters responsible for the backward bifurcation phenomenon were negligible, the the effective reproduction number is less than unity.