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Higher order multi-dimensional extensions of Cesàro theorem

Centro Vito Volterra Facultà di Economica, Università di Tor Vergata, Via di Tor Vergata, 00133 Roma, Italy

E-mail Address: accardi@volterra.mat.uniroma.it

Department of Mathematics, Research Institute of Mathematical Finance, Chungbuk National University, Cheongju 361-763, Korea

E-mail Address: uncigji@chungbuk.ac.kr

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, and

Kimiaki Saitô

Department of Mathematics, Meijo University, Nagoya 468, Japan

E-mail Address: ksaito@meijo-u.ac.jp

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https://doi.org/10.1142/S0219025715500307Cited by:5 (Source: Crossref)

Abstract

The Cesàro theorem is extended to the cases: (1) higher order Cesàro mean for sequence (discrete case); and (2) higher order, multi-dimensional and continuous Cesàro mean for functions. Also, we study the Cesàro theorem for the case of positive-order.

Communicated by O. Smolyanov

Keywords:

AMSC: 40G05

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