Cesro Summable and Statistically Convergent Sequences in Polya's Sense

This paper introduces and explores the concepts of Polya summability, strongly Polya summability, and statistical convergence in the Polya sense, establishing their relationships with classical summability methods, particularly Cesaro summability. We provide sufficient conditions for their equivalence, highlight key distinctions, and demonstrate these results through explicit examples. Notably, while every Cesaro summable sequence is Polya summable, the converse does not always hold. Additionally, we examine the connection between strongly Polya summable and Polya statistically convergent sequences, particularly for bounded and unbounded cases.