In the present paper, a novel absolute summability method, denoted by |Cq,θ|s, is introduced for double sequences via the q-Cesàro matrix. The study also focuses on determining the necessary and sufficient conditions for various inclusion relations, as well as comparing this method with existing absolute summability methods. In particular, the implications |Cp,ϕ|⇒|Cq,θ|s, |Cq,θ|s⇒|Cp,ϕ|, and |Cp,ϕ|s⇒|Cq,θ|s are fully characterized. The obtained results extend known summability frameworks for double series and highlight the role of q-analogues in providing a flexible and unifying approach to absolute summability theory.
Fadime Gökçe (Mon,) studied this question.