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)].


39B82 Stability, separation, extension, and related topics for functional equations
39B55 Orthogonal additivity and other conditional functional equations
Full Text: DOI


[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
[8] Ziółkowski, M., On conditional Jensen equation, Demonstratio Math., 34, 809-818 (2001) · Zbl 0995.39007
[10] Bourgin, D. G., Classes of transformations and bordering transformations, Bull. Amer. Math. Soc., 57, 223-237 (1951) · Zbl 0043.32902
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.