arXiv subjects

Erdal Bayram

Publications and source records attributed to Erdal Bayram.

3 recordsLinked to original sources

arXiv2025

Statistical order convergence of operators on Riesz Spaces

This paper introduces statistical order convergence and its pointwise variant for sequences of order bounded operators between Riesz spaces. We establish fundamental properties: uniqueness of the limit, stability under lattice operations, and a characterization via natural density linking it to classical order convergence. Explicit examples show that statistical order convergence is strictly weaker than order convergence, confirming that this concept provides a proper extension of operator-theoretic convergence notions. The results preserve essential lattice structures and open avenues for further research in unbounded convergence and Banach lattice theory.

math.FA↗

arXiv2024

Introducing Statistical Operators: Boundedness, Continuity, and Compactness

Many studies have been conducted on statistical convergence, and it remains an area of active research. Since its introduction, statistical convergence has found applications many fields. Nevertheless, there is a shortage of research related to operator theory. As far as we know, no studies have focused on continuous, bounded, and compact operators, which are fundamental concepts in mathematics. We explore the notions of statistical boundedness, continuity, and compactness of operators between normed spaces, establishing connections between these concepts and their counterparts in traditional normed space theory. Additionally, we provide examples and results that demonstrate the behavior and implications of statistical convergence in the context of operators.

math.FA↗

arXiv2023

On Statistical Convergence Of Order $α$ In Partial Metric Spaces

The present study introduces the notions of statistical convergence of order $α$ and strong $p-$ Cesàro summability of order $α$ in partial metric spaces. Also, we examine the inclusion relations between these concepts. In addition, we introduce the notion of $λ-$% statistical convergence of order $α$ in partial metric spaces while providing relations linked to these sequence spaces.

math.GM↗