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Demonstratio Mathematica

Editor-in-Chief: Vetro, Calogero

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CiteScore 2018: 0.47
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Volume 51, Issue 1


On the stability of a Cauchy type functional equation

Jung Rye Lee / Abbas Najati / Choonkil Park / Themistocles M. Rassias
Published Online: 2018-12-05 | DOI: https://doi.org/10.1515/dema-2018-0026


In this work, the Hyers-Ulam type stability and the hyperstability of the functional equationare proved.

Keywords: Hyers-Ulam stability; additive mapping; hyperstability; topological vector space

MSC 2010: 39B82; 34K20; 26D10


  • [1] Ulam S. M., Problems in Modern Mathematics, Chapter VI, Science ed., Wiley, New York, 1940Google Scholar

  • [2] Hyers D. H., On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A., 1941, 27(4), 222-224CrossrefGoogle Scholar

  • [3] Aoki T., On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan, 1950, 2(1-2), 64-66Google Scholar

  • [4] Rassias Th. M., On the stability of the linear mapping in Banach spaces, Proc. Am. Math. Soc., 1978, 72, 297-300Google Scholar

  • [5] Brzdek J., Fechner W., Moslehian M. S., Sikorska J., Recent developments of the conditional stability of the homomorphism equation, Banach J. Math. Anal., 2015, 9(3), 278-326Web of ScienceGoogle Scholar

  • [6] Brzdek J., Popa D., Rasa I., Xu B., Ulam Stability of Operators, Mathematical Analysis and its Applications, v. 1, Academic Press, Elsevier, Oxford, 2018Google Scholar

  • [7] Czerwik S., Functional Equations and Inequalities in Several Variables, World Scientific, River Edge, NJ, 2002Google Scholar

  • [8] Gordji M. E., Najati A., Approximately J*-homomorphisms: a fixed point approach, J. Geom. Phys., 2010, 60, 809-814Google Scholar

  • [9] Forti G. L., Hyers-Ulam stability of functional equations in several variables, Aequationes Math., 1995, 50(1-2), 143-190Google Scholar

  • [10] Hyers D. H., Isac G., Rassias Th. M., Stability of Functional Equations in Several Variables, Birkhäuser, Basel, 1998Web of ScienceGoogle Scholar

  • [11] Jung S., Hyers-Ulam-Rassias stability of functional equations in nonlinear analysis, Springer Optimization and its Applications, 48, Springer, New York, 2011Google Scholar

  • [12] Najati A., Homomorphisms in quasi-Banach algebras associated with a pexiderized Cauchy-Jensen functional equation, Acta Math. Sin. (Engl. Ser.), 2009, 25(9), 1529-1542CrossrefGoogle Scholar

  • [13] Najati A., Park C., On the stability of an n-dimensional functional equation originating from quadratic forms, Taiwanese J. Math., 2008, 12(7), 1609-1624Google Scholar

  • [14] Najati A., Rassias Th. M., Stability of a mixed functional equation in several variables on Banach modules, Nonlinear Anal.- TMA, 2010, 72(3-4), 1755-1767Google Scholar

  • [15] Rassias Th. M., On the stability of functional equations and a problem of Ulam, Acta Appl. Math., 2000, 62(1), 23-130Google Scholar

  • [16] Kannappan Pl., Sahoo P. K., Cauchy difference - a generalization of Hosszú functional equation, Proc. Nat. Acad. Sci. India, 1993, 63(3), 541-550Google Scholar

  • [17] Gajda Z., On stability of additive mappings, Int. J. Math. Sci., 1991, 14(3), 431-434.CrossrefGoogle Scholar

About the article

Received: 2018-05-31

Accepted: 2018-11-11

Published Online: 2018-12-05

Published in Print: 2018-11-01

Citation Information: Demonstratio Mathematica, Volume 51, Issue 1, Pages 323–331, ISSN (Online) 2391-4661, DOI: https://doi.org/10.1515/dema-2018-0026.

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© by Jung Rye Lee, et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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