×

zbMATH — the first resource for mathematics

Refined Hyers–Ulam approximation of approximately Jensen type mappings. (English) Zbl 1112.39025
The paper proves a refinement of the Hyers approximations for the Ulam stability problem in the case of Jensen-type mappings.

MSC:
39B82 Stability, separation, extension, and related topics for functional equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Aczél, J., Lectures on functional equations and their applications, (1966), Academic Press New York and London · Zbl 0139.09301
[2] Borelli, C.; Forti, G.L., On a general Hyers-Ulam stability result, Internat. J. math. sci., 18, 229-236, (1995) · Zbl 0826.39009
[3] Bourgin, D.G., Classes of transformations and bordering transformations, Bull. amer. math. soc., 57, 223-237, (1951) · Zbl 0043.32902
[4] Cholewa, P.W., Remarks on the stability of functional equations, Aequationes math., 27, 76-86, (1984) · Zbl 0549.39006
[5] Czerwik, St., On the stability of the quadratic mapping in normed spaces, Abh. math. sem. univ. Hamburg, 62, 59-64, (1992) · Zbl 0779.39003
[6] Drljevic, H., On the stability of the functional quadratic on A-orthogonal vectors, Publ. inst. math. (beograd) (N.S.), 36, 50, 111-118, (1984) · Zbl 0598.65029
[7] Fenyö, I., Osservazioni su alcuni teoremi di D.H. Hyers, Istit. lombardo accad. sci. lett. rend. A, 114, 1980, 235-242, (1982) · Zbl 0513.39008
[8] Fenyö, I., On an inequality of P.W. cholewa, (), 277-280
[9] Forti, G.L., Hyers-Ulam stability of functional equations in several variables, Aequationes math., 50, 143-190, (1995) · Zbl 0836.39007
[10] Gajda, Z.; Ger, R., Subadditive multifunctions and Hyers-Ulam stability, () · Zbl 0639.39014
[11] P. Gavruta, An answer to a question of John M. Rassias concerning the stability of Cauchy equation, in: Advances in Equations and Inequalities, Hadronic Math. Series, USA, 1999, pp. 67-71
[12] Gruber, P.M., Stability of isometries, Trans. amer. math. soc. USA, 245, 263-277, (1978) · Zbl 0393.41020
[13] Hyers, D.H.; Hyers, D.H., The stability of homomorphisms and related topics, (), 27, 140-153, (1941) · JFM 67.0424.01
[14] Jung, S.-M., On the Hyers-Ulam stability of the functional equations that have the quadratic property, J. math. anal. appl., 222, 126-137, (1998) · Zbl 0928.39013
[15] Malliavin, P., Stochastic analysis, (1997), Springer Berlin · Zbl 0878.60001
[16] Rassias, J.M., On approximation of approximately linear mappings by linear mappings, J. funct. anal., 46, 126-130, (1982) · Zbl 0482.47033
[17] Rassias, J.M., On approximation of approximately linear mappings by linear mappings, Bull. sci. math., 108, 445-446, (1984) · Zbl 0599.47106
[18] Rassias, J.M., Solution of a problem of Ulam, J. approx. theory, 57, 268-273, (1989) · Zbl 0672.41027
[19] Rassias, J.M., Complete solution of the multi-dimensional problem of Ulam, Discuss. mathem., 14, 101-107, (1994) · Zbl 0819.39012
[20] Rassias, J.M., Solution of the Ulam stability problem for Euler-Lagrange quadratic mappings, J. math. anal. appl., 220, 613-639, (1998) · Zbl 0928.39014
[21] Rassias, J.M., On the Ulam stability of mixed type mappings on restricted domains, J. math. anal. appl., 276, 747-762, (2002) · Zbl 1021.39015
[22] Rassias, J.M.; Rassias, M.J., On the Ulam stability of Jensen and Jensen type mappings on restricted domains, J. math. anal. appl., 281, 516-524, (2003) · Zbl 1028.39011
[23] Rassias, J.M., Asymptotic behavior of mixed type functional equations, Austral. J. math. anal. appl., 1, 1, 1-21, (2004) · Zbl 1060.39033
[24] Rassias, J.M., The Ulam stability problem in approximation of approximately quadratic mappings by quadratic mappings, J. ineq. pure appl. math., 5, 3, 1-9, (2004) · Zbl 1055.39041
[25] Rassias, J.M.; Rassias, M.J., Asymptotic behavior of alternative Jensen and Jensen type functional equations, Bull. sci. math., 129, 7, 545-558, (2005) · Zbl 1081.39028
[26] Ulam, S.M., Problems in modern mathematics, (1964), Wiley-Interscience New York, (Chapter VI) · Zbl 0137.24201
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.