Strongly Statistical Convergence of Order \alpha in Metric Spaces

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This paper introduces the concepts of M-strongly statistical convergence and [M]_d^α-summability of order α in metric spaces (X,d), where M denotes a non-negative infinite matrix. The relationship between these newly defined notions and M-strong convergence is examined in detail. Conditions ensuring the uniqueness of limits for M-strongly statistically convergent sequences are established. Also, we propose the definition of M-strongly statistical Cauchy sequences of order α and study their connection to M-strongly statistical convergence. Finally, we introduce M-strongly statistical bounded sequences of order α in metric spaces.