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Multidimensional Linear Functional Connected with Double Strong Cesàro Summability

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Abstract

In 1964 Borwein presented functional characterization of the normed linear spaces wp and Wp. These two spaces are clearly linked to Cesàro summability [C, 1] in particular it should be noted that a sequence x in wp if and only if x is Cesàro summable. The goal of this paper includes extension of these notions to double function space thus producing multidimensional analog of Borwein’s results.

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Acknowledgement

The second author is thankful to TUBITAK for a one year Visiting Scientist position at the University of North Florida, Jacksonville, U.S.A. where this work was done during 2017-2018.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of North Florida Jacksonville, Florida, 32224, USA

    Richard F. Patterson

  2. Department of Mathematics, Sakarya University, Sakarya, Turkey

    Rabia Savas

  3. Department of Mathematics, Usak University, Usak, Turkey

    Ekrem Savas

Authors
  1. Richard F. Patterson
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  2. Rabia Savas
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  3. Ekrem Savas
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Correspondence to Richard F. Patterson.

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Patterson, R.F., Savas, R. & Savas, E. Multidimensional Linear Functional Connected with Double Strong Cesàro Summability. Indian J Pure Appl Math 51, 143–153 (2020). https://doi.org/10.1007/s13226-020-0390-z

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  • DOI: https://doi.org/10.1007/s13226-020-0390-z

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