Earthline Journal of Mathematical Sciences

Frequency-dependent Symmetric Hybrid Multistep Method with Bounded Amplitude Error for Stiff and Oscillatory ODEs

2025-11-13T16:22:30+00:00

This paper considers a new fourth-order frequency-dependent symmetric hybrid linear multistep method for oscillatory second-order differential equations. The proposed method achieves minimal phase-lag and bounded amplitude error, which accurately reproduces orbital trajectories, and requires fewer function evaluations. Numerical experiment confirms improved efficiency, accuracy, and long-term stability over some existing methods in the literature.

Extension and Correction of an Inequality Similar to the Hardy-Hilbert Integral Inequality

2025-11-18T17:18:38+00:00

In this article, we present an extension to the Hardy-Hilbert integral inequality. This extension incorporates a multivariate parametric power-ratio function. The original formulation of the inequality is also included, along with a correction.

Sustainable Inventory Models for Raw Material Procurement: Integrating Environmental Resource Management in Manufacturing

2025-11-19T16:39:14+00:00

Efficient raw material procurement systems play a critical role in advancing environmental sustainability in manufacturing industries. This study presents mathematical inventory models designed to optimize procurement decisions while minimizing environmental impacts such as waste, excessive resource consumption, and energy use. By incorporating deterministic and variable demand scenarios, the models allow manufacturers to align inventory levels with both production needs and sustainable resource use strategies. The raw material procurement inventory model uses two major time elements (periods and circles) to describe procurement and replenishment quantities from several possible sources. Periods are the elapsed time elements between reviews of the stock position while circle is the number of periods occurring between successive procurement actions associated with a sequence of decisions over a period of time in which demand varies. Results from the numerical illustration show that optimized inventory management not only reduces procurement costs but also supports environmentally responsible operations. These findings highlight the synergy between operational efficiency and environmental stewardship in industrial systems.

Extension of Banach Contraction Mapping Principle in Multiplicative Cone Pentagonal Metric Space to a Pair of Two Self Mappings

2025-11-20T17:00:01+00:00

In this paper we combine the notions of multiplicative metric space [6] and cone pentagonal metric space [5] to form multiplicative cone pentagonal metric space. We prove a variant of the Banach contraction mapping theorem under two self-maps in this new space. Some corollaries are consequences of the main result, and some conjectures conclude the paper.

New Aspects of Extended General Equilibrium Inclusions

2025-11-24T02:00:17+00:00

Some new classes of extended general equilibrium inclusions are introduced and investigated. We have established the equivalence between the general equilibrium inclusions and the fixed point problems, which is used to discuss the unique existence of the solution. Using various techniques such as resolvent methods, dynamical systems coupled with finite difference approach, we suggest and analyze a number of new multi step methods for solving equilibrium inclusions. Convergence analysis of these methods is investigated under suitable conditions. Sensitivity analysis is also investigated. Various special cases are discussed as applications of the main results. Several open problems are suggested for future research.

Two New Contributions to the Three-dimensional Hardy-Hilbert-type Integral Inequalities

2025-11-26T15:54:38+00:00

The Hardy-Hilbert integral inequality is one of the most celebrated results in mathematical analysis, inspiring numerous variants and extensions. In this paper, we further advance the study of three-dimensional Hardy-Hilbert-type integral inequalities by proving two new theorems. One of these is notable for its inclusion of a maximum function, a feature rarely encountered in this three-dimensional context. The associated constant factors are determined explicitly and detailed proofs are provided, without recourse to special functions.

(α, β)-Reich Contraction Mapping Theorem in Multiplicative Metric Space

2025-12-08T15:42:33+00:00

In this paper, we introduce the notion of (α, β)-Reich contraction, and obtain a fixed point theorem for such mappings in the setting of multiplicative metric space. Moreover, we give a Corollary as a consequence of the main result.

On Two Convex Weighted Integral Inequalities

2025-12-23T16:17:06+00:00

Thanks to their wide range of applications in mathematics, convex integral inequalities continue to inspire new research.
In this paper, we present weighted generalizations of two such modern results, thereby extending their scope and applicability.
Several examples involving polynomial and trigonometric (sine) weight functions are provided.

Approximation of Random Homomorphisms and Random Derivations on Banach Algebras via Direct and Fixed Point Methods

2026-01-05T16:50:42+00:00

In this paper, we prove the approximation of homomorphisms and derivations related to the following functional equation:
\[
f(2x+y) + f(2x-y)
= f(x+y) + f(x-y) + 2f(2x) - 2f(x).
\]
The results are obtained in random Banach algebras by means of the direct method and the fixed point method.

Fourier Series and Recurrence Relations for Zeta Functions

2026-01-06T16:35:12+00:00

This article explores the connection between Fourier series and various zeta functions, including the Riemann zeta function and its generalizations. Specifically, we derive recurrence formulas for even and odd values of zeta functions using Fourier expansions, extending these results to the Hurwitz zeta function.

Reich Contraction Mapping Theorem of Integral Type in Metric Spaces with w-Distance

2026-01-09T16:29:35+00:00

In this paper, we introduce the notion of Reich contraction of integral type in metric spaces with w-distance and prove a fixed point theorem. Some conjectures conclude the paper.