A new type of convergence in partial metric spaces

Nuray, Fatih
Nuray Yıldırım, Elif

Hilbert Journal of Mathematical Analysis
Vol. 3 No. 2 (2025): Hilbert J. Math. Anal.

In this paper, we introduce the concept of deferred statistical convergence in partial metric spaces (pms), extending classical notions of statistical convergence and summability. We define deferred Cesaro summability and investigate its fundamental properties. Connections between statistical convergence and deferred Cesaro summability are explored, including inclusion relationships and strictness. Additionally, we establish conditions under which deferred summability implies statistical convergence and vice versa. Examples and theorems are provided to illustrate the applicability and relevance of these concepts in partial metric spaces.