On Continuities via P-Statistical Convergence

This study investigates the concepts of P-statistical continuity (statistical continuity with respect to power series method) and P-statistical ward continuity (statistical ward continuity with respect to power series method) within the framework of power series methods, which extend the scope of statistical convergence beyond classical matrix methods. In the background, the limitations of traditional methods in capturing generalized continuity behaviors are explored and the use of power series as a versatile tool is motivated. Connections between these specialized forms of continuity and standard continuity are established, providing proofs and detailed properties. The results include several foundational theorems characterizing P-statistical continuity and ward continuity under various settings. These findings contribute to a more profound comprehension of continuity concepts within the context of regular summability methods. MSC: 26A15, 40A05, 40G10.