On Statistical Convergence of Order α in Partial Cone Metric Spaces

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 α and λ-statistical convergence of order α and demonstrating their relationships. Furthermore, we define the statistical Cauchy sequences of order α and the λ-statistical boundedness of order α and examine some inclusion theorems. Additionally, in partial cone metric spaces, we show that a non-convergent sequence is statistically convergent of order α.