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The Generalized Hyperstability of General Linear Equation in Quasi-2-Banach Space

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Abstract

In this paper, we study the hyperstability for the general linear equation

$$f(ax + by) = Af(x) + Bf(y)$$

in the setting of complete quasi-2-Banach spaces. We first extend the main fixed point result of Brzdȩk and Ciepliński (Acta Mathematica Scientia, 2018, 38B(2): 377–390) to quasi-2-Banach spaces by defining an equivalent quasi-2-Banach space. Then we use this result to generalize the main results on the hyperstability for the general linear equation in quasi-2-Banach spaces. Our results improve and generalize many results of literature.

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Acknowledgements

The authors are thankful to Professor N. V. Dung, Dong Thap University, Vietnam, for providing some material on the topic.

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Authors and Affiliations

  1. School of Mathematics, Thapar Institute of Engineering and Technology, Patiala, 147004, India

    Ravinder Kumar Sharma & Sumit Chandok

Authors
  1. Ravinder Kumar Sharma
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  2. Sumit Chandok
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Corresponding author

Correspondence to Sumit Chandok.

Additional information

The authors acknowledged to AISTDF, DST India for the research grant vide project No. CRD/2018/000017.

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Sharma, R.K., Chandok, S. The Generalized Hyperstability of General Linear Equation in Quasi-2-Banach Space. Acta Math Sci 42, 1357–1372 (2022). https://doi.org/10.1007/s10473-022-0406-3

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  • DOI: https://doi.org/10.1007/s10473-022-0406-3

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