On two conditional Pexider functional equations and their stabilities. (English) Zbl 1162.39018
The author solves two conditional Pexider functional equations and investigates their generalized Hyers-Ulam stability. Besides the references given in the paper, the reader can find related results in the book D. H. Hyers, G. Isac and Th. M. Rassias [Stability of functional equations in several variables. Birkhäuser (1998; Zbl 0907.39025)] and in the paper by P. Gavruta [J. Math. Anal. Appl. 184, No. 3, 431–436 (1994; Zbl 0791.47011)].
Reviewer: Paşc Găvruţă (Timişoara)
MSC:
| 39B82 | Stability, separation, extension, and related topics for functional equations |
| 39B55 | Orthogonal additivity and other conditional functional equations |
Keywords:
conditional functional equation; Hyers-Ulam-Rassias stability; Pexider functional equationsReferences:
| [1] | Alsina, C.; Garcia-Roig, J. L., On a conditional Cauchy equation on rhombuses, (Functional Analysis, Approximation Theory and Numerical Analysis, vol. 5-7 (1994), World Sci. Publishing: World Sci. Publishing River Edge, NJ) · Zbl 0877.39015 |
| [2] | Szabó, Gy., A conditional Cauchy equation on normed spaces, Publ. Math. Debrecen, 42, 256-271 (1993) · Zbl 0807.39010 |
| [3] | James, R. C., Orthogonality in normed linear spaces, Duke Math. J., 12, 291-302 (1945) · Zbl 0060.26202 |
| [4] | James, R. C., Orthogonality and linear functionals in normed linear spaces, Trans. Amer. Math. Soc., 61, 265-292 (1947) · Zbl 0037.08001 |
| [5] | Ger, R.; Sikorska, J., On the Cauchy equation on spheres, Ann. Math. Sil., 11, 89-99 (1997) · Zbl 0894.39009 |
| [6] | Hyers, D. H., On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA, 27, 222-224 (1941) · Zbl 0061.26403 |
| [7] | J. Sikorska, Ortogonalna stabilność niektórych równań funkcyjnych, Ph.D., University of Silesia, Katowice, 1998 (in Polish); J. Sikorska, Ortogonalna stabilność niektórych równań funkcyjnych, Ph.D., University of Silesia, Katowice, 1998 (in Polish) |
| [8] | Ziółkowski, M., On conditional Jensen equation, Demonstratio Math., 34, 809-818 (2001) · Zbl 0995.39007 |
| [9] | J. Sikorska, Generalized stability of the Cauchy and Jensen functional equations on spheres, J. Math. Anal. Appl. (2008), doi:10.1016/j.jmaa.2008.04.046; J. Sikorska, Generalized stability of the Cauchy and Jensen functional equations on spheres, J. Math. Anal. Appl. (2008), doi:10.1016/j.jmaa.2008.04.046 · Zbl 1157.39019 |
| [10] | Bourgin, D. G., Classes of transformations and bordering transformations, Bull. Amer. Math. Soc., 57, 223-237 (1951) · Zbl 0043.32902 |
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