Earthline Journal of Mathematical Sciences

Bi-univalent Function Subfamilies Associated with the (p,q)-derivative Operator Subordinate to Lucas-Balancing Polynomials

Sondekola Rudra Swamy — 2025-02-04

In the open disc $\{\zeta\in\mathbb{C}:|\zeta| <1\}$ $=\mathfrak{D}$, we present a family of bi-univalent functions $g(\zeta)=\zeta+\sum\limits_{j=2}^{\infty}d_j\zeta^j$ associated with the $(p,q)$-derivative operator and Lucas-Balancing polynomials. For members of this family, we obtain the upper bounds for $|d_2|$, $|d_3|$, and $|d_3-\xi d_2^2|$, $\xi \in\mathbb{R}$. The new implications of the main results are also discussed, along with relevant connections to earlier research.

General Dynamical Systems and Variational Inequalities

Muhammad Aslam Noor — 2025-02-12

In this paper, we introduce and consider a new second order dynamical system for solving general variational inequalities. Using the forward backward finite difference schemes, we suggest some new multi-step
iterative methods for solving the variational inequalities and their variants forms. Convergence analysis is investigated under certain mild conditions. We also use the change of variable method to establish the equivalence between the complementarity problems and the fixed point problems. The alternate formulation can exploited to consider the dynamical systems and study the stability properties of the solution. Since the variational inequalities are equivalent to the complementarity problems, our results can be used to develop new techniques for them. It is an interesting problem to compare these methods with other technique for solving variational inequalities and related optimizations for further research activities.

Banach Contraction Mapping Theorem in (α, β, c)-Interpolative Metric Space

Clement Boateng Ampadu — 2025-02-15

In this paper we introduce the notion of (α, β, c)-interpolative metric space as an extension of (α, c)-interpolative metric space [Karapınar, E. (2023). An open discussion: Interpolative metric spaces. Advances in the Theory of Nonlinear Analysis and Its Applications, 7(5), 24-27]. The (α, β, c)-interpolative metric space can be regarded as a generalization of generalized metric space [Branciari, A. (2000). A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces.
Publicationes Mathematicae Debrecen, 57(1), 31-37]. Additionally, we prove the Banach contraction mapping theorem [Banach, S. (1922). Sur les opérations dans les ensembles abstraits et leur applications aux équations intégrales. Fundamenta Mathematicae, 3, 133-181] in (α, β, c)-interpolative metric space.

Optimal Investment and Debt Management Strategies in the Presence of Inflation Risks for a DC Pension Scheme

C. B. Ibe — 2025-02-17

This paper derives the optimal debt ratio, portfolio strategies and consumption rate for a Pension Fund Administrator (PFA) in a defined contributory (DC) pension scheme. Four asset classes were considered which include riskless asset, inflation-linked bonds, stocks and housing. Five background risks which include inflation, stock, housing, income growth rate and salary risks are considered. The plan member contributes a proportion of his or her stochastic salary into the scheme. The PFA make further effort to borrow money to finance her investment to ensure maximum returns. The contribution of the plan member in addition to borrowed capital is invested in financial and non-financial (housing) assets. In this paper, the real wealth process of the PFA is considered. The problem is formulated as a bi-objective stochastic control problem. The resulting Hamilton-Jacobi-Bellman (HJB) equation was solved using dynamic programming approach for stochastic process. This paper aims at (i) maximize the total expected discounted utility of consumption and debt of the PFA in an infinite time horizon, (ii) determine the optimal debt ratio and optimal consumption plan of the PFA, (iii) determine the optimal investment strategies for a PFA who invest in an economy that is exposed to five background risks. Using dynamic programming approach, we derive the optimal debt ratio, optimal consumption plan, optimal investment in inflation-linked bonds, stocks and housing for a PFA that chooses the power utility function. We found that the optimal debt ratio depends directly on the optimal real wealth. We also found that the optimal investment in stocks, housing and inflation-linked bonds depend on inflation, stock, salary, housing and income growth rate risks. Numerical implementation of the models using empirical data are presented.

Block Hybrid Trapezoidal-type Methods for Solving Initial Value Problems in Ordinary Differential Equations

E. Igbinovia — 2025-02-18

In solving ordinary differential equations, tackling stiff problems necessitates the application of robust numerical methods endowed with A-stability properties. To circumvent the constraints posed by the Dahlquist barrier theorem and mitigate errors arising from step-by-step implementation of linear multistep methods, block hybrid schemes have been introduced. This study focuses on the development of novel block schemes designed for the direct approximation of solutions to stiff initial value problems. The methods proposed herein leverage both interpolation and collocation, enhancing their consistency, convergence, and accuracy in solving initial value problems. The efficacy of the devised methods is demonstrated through a comprehensive analysis of stability regions for each of the constructed block algorithms. Notably, these stability regions are proven to be unbounded for order $p\leq 15$. Comparative assessments reveal their competitiveness with existing methods. In fact, this research introduces innovative approaches to address the challenges posed by stiff initial value problems, offering enhanced stability and accuracy in comparison to established methods.

Fekete-Szegö Problem for Univalent Functions and Quasiconformal Extension

Jinlong Yang — 2025-02-24

Via Löwner theories, by Becker's and Betker's conditions on Herglotz function which give sufficient conditions for univalent functions admitting $k$-quasiconformal extension to the complex plane, we define two subclasses denoted by $S_{k}^{B}$ and $S_{k}^{BT}$. Then we solve the Fekete-Szegö problem on these two subclasses.

Enhancing Spatial Autoregressive Models with Bootstrap Techniques: A Methodological Investigation into Bias, Precision, and Sample Size Effects

F. E. Itiveh — 2025-02-27

This study introduces and evaluates two novel bootstrap-enhanced methods: the Bootstrap Simultaneous Autoregressive Lag Model (BSALM) and the Bootstrap Simultaneous Autoregressive Error Model (BSAEM), within the framework of classical Spatial Simultaneous Autoregressive (SAR) models. Using simulated datasets from normal distributions across varying sample sizes ( 10 to 500) and secondary real-world data, the study examines their effectiveness in addressing spatial dependencies. The study’s objectives include assessing bias, standard errors, variability, and the influence of sample size on model efficiency. Results demonstrate that both methods significantly reduce bias and variability as sample size increases, highlighting the critical role of adequate data dimensions in spatial analysis. BSALM consistently outperformed BSAEM in bias reduction, while BSAEM proved more adept at capturing complex spatial interdependencies despite exhibiting higher variability. Challenges with smaller datasets revealed increased biases and variability, emphasizing the importance of cautious interpretation in such scenarios. Real-world applications underscored dataset-specific performance variations, with BSALM excelling in bias correction and BSAEM managing intricate spatial structures. By integrating bootstrap techniques into SAR modelling, this study provides practical tools for enhancing predictive accuracy and model validation. While computational demands remain a consideration, these findings offer valuable insights into balancing bias, variability, and efficiency, paving the way for future advancements in spatial econometric analysis.