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This work identifies necessary and sufficient conditions for matrix summability in infinite series, suggesting critical links between the criteria involved.
Earlier works have established the conditions under which the series \(∑\)\(a_n\)\(γ\)\(_n\) is ϕ − | F, μ; τ |k summable, provided that the series \(∑\)\(a_n\) is summable by ϕ − | E, μ; τ |. In this study, we present the necessary and sufficient criteria ensuring ϕ−| F, μ; τ | summability of \(∑\)\(a_n\)\(γ\)\(_n\) whenever \(∑\)\(a_n\) is summable by ϕ−| E, μ; τ |k, where E = (env) and F = (fnv) denote two positive normal matrices, k ≥ 1, τ ≥ 0, and the inequality −μ(τk + k − 1) + k > 0 holds.
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Bağdagül Kartal Erdoğan (2025) studied this question.
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