Some remarks on the stability of the multi-Jensen equation

• Autorzy: Jens Schwaiger
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Multi-Jensen functions; Stability

Kategorie tematyczne

• 39B52: Equations for functions with more general domains and/or ranges

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 5
• Strony: 966-971

Daty

wydano

2013-05-01

online

2013-03-14

Twórcy

autor

Jens Schwaiger

• Karl-Franzens Universität

Bibliografia

• [1] Brzdek J., The Cauchy and Jensen differences on semigroups, Publ. Math. Debrecen, 1996, 48(1–2), 117–136
• [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
• [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
• [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
• [6] Forti G.L., Schwaiger J., Stability of homomorphisms and completeness, C. R. Math. Rep. Acad. Sci. Canada, 1989, 11(6), 215–220
• [7] Jung S.-M., Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis, Springer Optim. Appl., 48, Springer, New York, 2011
• [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
• [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

Identyfikatory

DOI

10.2478/s11533-013-0215-y