Earthline Journal of Mathematical Sciences

Generalized Sasakian Manifolds: Pseudosymmetry Characterizations Related to Some Important Curvature Tensors

2026-02-02T14:53:27+00:00

In this study, generalized Sasakian space forms are examined on $W_{5}-,W_{6},W_{7}$, and $W_{9}-$ curvature tensors. Moreover, special curvature conditions with the help of $W_{5}-,W_{6},W_{7}$, $W_{9}-$ pseudosymmetry and $W_{5}-,W_{6},W_{7}$, $W_{9}-$ Ricci pseudosymmetry are defined. The behavior for the generalized Sasakian space form is then represented in accordance with these concepts.

Refinements and Extensions of Classical Integral Inequalities: Hölder, Hardy, Minkowski, Clarkson, and Schweitzer

2026-02-02T16:05:22+00:00

Integral inequalities are a fundamental part of modern mathematical analysis and the theory of function spaces. In this paper, we present several refinements and extensions to classical integral inequalities, with a particular focus on those of Hölder, Hardy, Minkowski, Clarkson, and Schweitzer. First, we apply Hölder's inequality to find new refined bounds. Then, we establish Hölder-type inequalities using extended Young's inequalities. Consequently, we derive Hardy-type derivative inequalities with an optimal weight factor. After that, we introduce the Minkowski-Clarkson relation and variation for two functions. Lastly, we formulate a weighted generalisation of Schweitzer's inequality incorporating parametric functions. Concrete examples involving the beta and gamma functions demonstrate the sharpness and applicability of the proposed bounds, showing measurable improvements upon their classical counterparts.

A Collection of Inequalities Involving Power Exponential and Logarithmic Functions

2026-02-03T14:38:12+00:00

Power exponential functions and logarithmic functions, are two classes of functions which are ubiquitous in Mathematical Analysis with lots of contemporary applications. In this article, interpolation type inequalities involving power exponential and logarithmic functions are derived, and the techniques applied to derive these inequalities are not the usual that somebody encounters in the literature. All the results are derived using functional estimates and popular integral inequalities such as the Chebyshev integral inequality version. Most of the authors in the literature use monotonicity properties and series expansions, whereas in the current work the inequalities are rigorously proved using predominantly functional estimates, which is a technique more encountered in Functional Analysis and PDEs. To the best of our knowledge, the inequalities are new in the literature and the methods to yield the inequalities is novel and non trivial. This work serves in dual manner, having a research and pedagogical purpose and contributes to the field of Mathematical Analysis and Inequalities.

A Dual Sampling Approach for Improved Classifier Performance on Imbalance Datasets

2026-02-05T17:03:23+00:00

Background: The inability of traditional machine learning models to adequately classify minority instances in imbalanced datasets is a known challenge that militate against the successful application of these models in several real-world domains. To address this problem, several techniques including data sampling are mostly used. Though reducing the imbalance ratio via sampling is reported to improve classifier performance, most approaches do not consider the intra-class distribution of instances while sampling, which often lead to loss of significant information or on the contrary cause data redundancy. Methods: This study proposes a novel Dual Sampling Technique (DST) that minimises these challenges and enhances classifier performance on imbalance datasets. The technique proceeds by first clustering a training set into a number of clusters determined a priori using the elbow method. Sampling ratios are computed from each cluster and either random undersampling or a novel average oversampling technique or both are used to perform sampling in each cluster depending on the imbalance ratio. The resulting datasets are used to train Random Forest, Decision Tree and K-Nearest Neighbor classifiers and their performance evaluated. Findings: Experimental results showed that the performance of the classifiers significantly improved in most cases when the proposed technique is used to sample the training set prior to model building than when Random Undersampling (RUS), Random Oversampling (ROS), Synthetic Minority Oversampling Technique (SMOTE) and Cluster-Based Undersampling (CBU) are used. Novelty: The novelty of the proposed technique lies in the exploration of a unique concept that sought to minimise the imbalance ratio in datasets while maintaining their natural distribution by uniquely performing both undersampling and oversampling on the same dataset.

Chatterjea Polynomial Contraction Mapping Theorem in Metric Spaces with Application

2026-02-09T16:02:30+00:00

In this paper, we introduce the notion of polynomial Chatterjea contraction mapping in metric spaces, and obtain a fixed point theorem. Some consequences of the main result and a conjecture are stated. The conjecture is illustrated with an example, and the conjecture is used to show existence and uniqueness of solutions for a certain class of fractional differential equations.