# Some remarks on the stability of the multi-Jensen equation

Open Mathematics (2013)

- Volume: 11, Issue: 5, page 966-971
- ISSN: 2391-5455

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topJens Schwaiger. "Some remarks on the stability of the multi-Jensen equation." Open Mathematics 11.5 (2013): 966-971. <http://eudml.org/doc/269254>.

@article{JensSchwaiger2013,

abstract = {First a stability result of Prager-Schwaiger [Prager W., Schwaiger J., Stability of the multi-Jensen equation, Bull. Korean Math. Soc., 2008, 45(1), 133–142] is generalized by admitting more general domains of the involved function and by allowing the bound to be not constant. Next a result by Cieplinski [Cieplinski K., On multi-Jensen functions and Jensen difference, Bull. Korean Math. Soc., 2008, 45(4), 729–737] is discussed. Finally a characterization of the completeness of a normed space in terms of stability requirements for multi-Jensen functions is presented.},

author = {Jens Schwaiger},

journal = {Open Mathematics},

keywords = {Multi-Jensen functions; Stability; multi-Jensen equation; completeness; stability; Banach space},

language = {eng},

number = {5},

pages = {966-971},

title = {Some remarks on the stability of the multi-Jensen equation},

url = {http://eudml.org/doc/269254},

volume = {11},

year = {2013},

}

TY - JOUR

AU - Jens Schwaiger

TI - Some remarks on the stability of the multi-Jensen equation

JO - Open Mathematics

PY - 2013

VL - 11

IS - 5

SP - 966

EP - 971

AB - First a stability result of Prager-Schwaiger [Prager W., Schwaiger J., Stability of the multi-Jensen equation, Bull. Korean Math. Soc., 2008, 45(1), 133–142] is generalized by admitting more general domains of the involved function and by allowing the bound to be not constant. Next a result by Cieplinski [Cieplinski K., On multi-Jensen functions and Jensen difference, Bull. Korean Math. Soc., 2008, 45(4), 729–737] is discussed. Finally a characterization of the completeness of a normed space in terms of stability requirements for multi-Jensen functions is presented.

LA - eng

KW - Multi-Jensen functions; Stability; multi-Jensen equation; completeness; stability; Banach space

UR - http://eudml.org/doc/269254

ER -

## References

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- [2] Bae J.-H., Park W.-G., On the solution of a bi-Jensen functional equation and its stability, Bull. Korean Math. Soc., 2006, 43(3), 499–507 http://dx.doi.org/10.4134/BKMS.2006.43.3.499 Zbl1113.39030
- [3] Cieplinski K., On multi-Jensen functions and Jensen difference, Bull. Korean Math. Soc., 2008, 45(4), 729–737 http://dx.doi.org/10.4134/BKMS.2008.45.4.729
- [4] Cieplinski K., Stability of the multi-Jensen equation, J. Math. Anal. Appl., 2010, 363(1), 249–254 http://dx.doi.org/10.1016/j.jmaa.2009.08.021 Zbl1211.39017
- [5] Forti G.L., Hyers-Ulam stability of functional equations in several variables, Aequationes Math., 1995, 50(1–2), 143–190 http://dx.doi.org/10.1007/BF01831117 Zbl0836.39007
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- [7] Jung S.-M., Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis, Springer Optim. Appl., 48, Springer, New York, 2011 Zbl1221.39038
- [8] Prager W., Schwaiger J., Multi-affine and multi-Jensen functions and their connection with generalized polynomials, Aequationes Math., 2005, 69(1–2), 41–57 http://dx.doi.org/10.1007/s00010-004-2756-4 Zbl1072.39025
- [9] Prager W., Schwaiger J., Stability of the multi-Jensen equation, Bull. Korean Math. Soc., 2008, 45(1), 133–142 http://dx.doi.org/10.4134/BKMS.2008.45.1.133 Zbl1151.39023

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