In this paper, the relationship between Abel and Cesàro convergence for interval-valued sequences and summability for interval-valued series is investigated. It is first shown that Cesàro convergence implies Abel convergence for interval-valued sequences. A Tauberian converse is then established by showing that Abel convergence implies Cesàro convergence when the endpoint sequences are bounded. These results are further extended to interval-valued series through their sequences of partial sums. In particular, interval-valued analogues of several classical Tauberian theorems are obtained by showing that Abel summability implies Cesàro summability under boundedness, nonnegativity, and the lower Landau condition on the sequence of partial sums. Consequently, classical Abel-Cesàro inclusion results and Tauberian theorems are extended to the interval-valued setting, providing a basis for further investigations of interval-valued summability methods.
Citation: Bağdagül Kartal Erdoğan. Inclusion relations between Abel and Cesàro summability in the interval-valued setting[J]. AIMS Mathematics, 2026, 11(9): 30566-30580. doi: 10.3934/math.20261211
In this paper, the relationship between Abel and Cesàro convergence for interval-valued sequences and summability for interval-valued series is investigated. It is first shown that Cesàro convergence implies Abel convergence for interval-valued sequences. A Tauberian converse is then established by showing that Abel convergence implies Cesàro convergence when the endpoint sequences are bounded. These results are further extended to interval-valued series through their sequences of partial sums. In particular, interval-valued analogues of several classical Tauberian theorems are obtained by showing that Abel summability implies Cesàro summability under boundedness, nonnegativity, and the lower Landau condition on the sequence of partial sums. Consequently, classical Abel-Cesàro inclusion results and Tauberian theorems are extended to the interval-valued setting, providing a basis for further investigations of interval-valued summability methods.
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Bağdagül Kartal Erdoğan. Inclusion relations between Abel and Cesàro summability in the interval-valued setting[J]. AIMS Mathematics, 2026, 11(9): 30566-30580. doi: 10.3934/math.20261211
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