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Turkish Journal of Mathematics

Author ORCID Identifier

ABDULLAH AYDIN: 0000-0002-0769-5752

RECEP TÜRK: 0000-0002-9469-5813

İREM GÜLER: 0009-0009-3455-8807

Abstract

This paper introduces a new concept of convergence, called statistical multiplicative uniform convergence, on Riesz algebras. This concept unifies three fundamental convergence types: statistical convergence, multiplicative convergence, and relatively uniform convergence. After establishing basic properties such as uniqueness, linearity, and compatibility with algebraic and lattice operations, we investigate its relationships with order convergence, statistical multiplicative order convergence, and relatively uniform convergence. In particular, we prove that statistical multiplica tive uniform convergence coincides with statistical multiplicative order convergence when an order unit exists. Moreover, for monotone sequences in Archimedean semiprime f-algebras, statistical multiplicative uniform convergence implies order convergence. We also study boundedness, Cauchy sequences, and completeness in this new setting. The results demonstrate that statistical multiplicative uniform convergence provides a natural and powerful tool for analysis in Riesz algebras, with potential applications in functional analysis and statistical limit theory.

DOI

10.55730/1300-0098.3681

Keywords

Statistical convergence, Riesz algebra, $st$-$mu$-convergence, uniform convergence, order convergence, Riesz spaces

First Page

781

Last Page

793

Publisher

The Scientific and Technological Research Council of Türkiye (TÜBİTAK)

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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