On Statistical Convergence of Order ? in Partial Cone Metric Spaces - Sarikaya, Süleyman; Kasap, Mithat; Altin, Yavuz; Altinok, Hifsi (Mdpi, 2026)
The importance of sequence spaces has increased with the emergence of various new convergence methods such as statistical convergence. On the other hand, partial metric spaces hold an important place in computer science, data science, and convergence analysis because they contain points whose distance from themselves is non-zero. For these reasons, in the present paper, we generalize the concept of statistical convergence, previously defined for cone metric spaces, to partial cone metric spaces, defining statistical convergence of order alpha and lambda-statistical convergence of order alpha and demonstrating their relationships. Furthermore, we define the statistical Cauchy sequences of order alpha and the lambda-statistical boundedness of order alpha and examine some inclusion theorems. Additionally, in partial cone metric spaces, we show that a non-convergent sequence is statistically convergent of order alpha.
Keywords: statistical convergence; cone metric spaces; partial metric spaces; partial cone metric spaces