Stability of generalized Jensen functional equation on a set of measure zero
DOI:
https://doi.org/10.4067/S0716-09172016000400007Keywords:
K-Jensen functional equation, Hyers-Ulam stability, ecuación funcional K-Jensen, estabilidad de Hyers-UlamAbstract
Let E is a complex vector space and F is real (or complex ) Banach space. In this paper, we prove the Hyers-Ulam stability for the generalized Jensen functional equation
References
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[2] J. A. Baker, A general functional equation and its stability, Proceeding of the American Mathematical Society, 133, pp. 1657-1664, (2005).
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[7] P. W. Cholewa, Remarks on the stability of functional equations, Aequationes mathematicae, 27, pp. 76-86, (1984).
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[12] P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, Journal of Mathematical Analysis and Applications, 184, pp. 431-436, (1994).
[13] D. H. Hyers, On the stability of the linear functional equation, Proceedings of the National Academy of Sciences, 27, pp. 222-224, (1941).
[14] D. H. Hyers and Th. M. Rassias, Approximate homomorphisms, Aequationes Mathematicae, 44, pp. 125-153, (1992).
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[16] K. W. Jun and Y. H. Lee, A generalization of the Hyers-Ulam-Rassias stability of Jensen0s equation, Journal of Mathematical Analysis and Applications, 238, pp. 305-315, (1999).
[17] S. M. Jung, On the Hyers-Ulam stability of the functional equations that have the quadratic property, Journal of Mathematical Analysis and Applications, 222, pp. 126-137, (1998).
[18] C. F. K. Jung, On generalized complete metric spaces, Bulletin of the American Mathematical Society, 75, pp. 113-116, (1969).
[19] R. Ã Lukasik, Some generalization of Cauchy0s and the quadratic functional equations, Aequationes Mathematicae, 83, pp. 75-86, (2012).
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[21] J. C. Oxtoby, Measure and Category, Springer, New-York (1980).
[22] Th. M. Rassias, On the stability of linear mapping in Banach spaces, Proceedings of the American Mathematical Society, 72, pp. 297-300, (1978).
[23] Th. M. Rassias, On the stability of the functional equations and a problem of Ulam, Acta Applicandae Mathematicae, 62, pp. 23-130, (2000).
[24] Th. M. Rassias and P. Semrl, ? On the behavior of mappings which do not satisfy Hyers-Ulam stability, Proceedings of the American Mathematical Society, 114, pp. 989-993, (1992).
[25] Th. M. Rassias, and J. Tabor, Stability of Mappings of Hyers-Ulam Type, Hardronic Press, (1994).
[26] J. M. Rassias, On the Ulam stability of mixed type mappings on restricted domains, Journal of Mathematical Analysis and Applications, 276, pp. 747-762, (2002).
[27] F. Skof, Local properties and approximations of operators, Rendiconti del Seminario Matematico e Fisico di Milano, 53, pp. 113-129, (1983).
[28] H. Stetkær, Functional equations involving means of functions on the complex plane, Aequationes Mathematicae, 56, pp. 47-62, (1998).
[29] S. M. Ulam, A Collection of Mathematical Problems, Interscience Publishers, 8(1960)
[2] J. A. Baker, A general functional equation and its stability, Proceeding of the American Mathematical Society, 133, pp. 1657-1664, (2005).
[3] N. Brillouet-Belluot, J. Brzd¸ ek, K. Ciepli` nski, On some recent developments in Ulam’s type stability, Abstract and Applied Analysis, (2012).
[4] J. Brzd¸ ek, On a method of proving the Hyers-Ulam stability of functional equations on restricted domains, The Australian Journal of Mathematical Analysis and Applications, 6, pp. 1-10, (2009).
[5] A. B. Chahbi, A. Charifi, B. Bouikhalene and S. Kabbaj, Nonarchimedean stability of a Pexider K-quadratic functional equation, Arab Journal of Mathematical Sciences, 21, pp. 67-83, (2015).
[6] A. Chahbi, M. Almahalebi, A. Charifi and S.Kabbaj Generalized Jensen functional equation on restricted domain, Annals of West University of Timisoara-Mathematics, 52, pp. 29-39, (2014).
[7] P. W. Cholewa, Remarks on the stability of functional equations, Aequationes mathematicae, 27, pp. 76-86, (1984).
[8] J. Chung, Stability of a conditional Cauchy equation on a set of measure zero, Aequationes mathematicae, 87, pp. 391-400, (2014).
[9] J. Chung and J. M. Rassias, Quadratic functional equations in a set of Lebesgue measure zero, Journal of Mathematical Analysis and Applications, 419, pp. 1065-1075, (2014).
[10] J. Chung and J. M. Rassias, On a measure zero Stability problem of a cyclic equation, Bulletin of the Australian Mathematical Society, 93, pp. 1-11, (2016).
[11] S. Czerwik, On the stability of the quadratic mapping in normed spaces, Abhandlungen aus dem Mathematischen Seminar der Universitat at Hamburg, 62, pp. 59-64, (1992).
[12] P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, Journal of Mathematical Analysis and Applications, 184, pp. 431-436, (1994).
[13] D. H. Hyers, On the stability of the linear functional equation, Proceedings of the National Academy of Sciences, 27, pp. 222-224, (1941).
[14] D. H. Hyers and Th. M. Rassias, Approximate homomorphisms, Aequationes Mathematicae, 44, pp. 125-153, (1992).
[15] D. H. Hyers, Transformations with bounded n-th differences, Pacific Journal of Mathematics, 11, pp. 591-602, (1961).
[16] K. W. Jun and Y. H. Lee, A generalization of the Hyers-Ulam-Rassias stability of Jensen0s equation, Journal of Mathematical Analysis and Applications, 238, pp. 305-315, (1999).
[17] S. M. Jung, On the Hyers-Ulam stability of the functional equations that have the quadratic property, Journal of Mathematical Analysis and Applications, 222, pp. 126-137, (1998).
[18] C. F. K. Jung, On generalized complete metric spaces, Bulletin of the American Mathematical Society, 75, pp. 113-116, (1969).
[19] R. Ã Lukasik, Some generalization of Cauchy0s and the quadratic functional equations, Aequationes Mathematicae, 83, pp. 75-86, (2012).
[20] A. Najati, S. M. Jung, Approximately quadratic mappings on restricted domains, Journal of Inequalities and Applications, (2010).
[21] J. C. Oxtoby, Measure and Category, Springer, New-York (1980).
[22] Th. M. Rassias, On the stability of linear mapping in Banach spaces, Proceedings of the American Mathematical Society, 72, pp. 297-300, (1978).
[23] Th. M. Rassias, On the stability of the functional equations and a problem of Ulam, Acta Applicandae Mathematicae, 62, pp. 23-130, (2000).
[24] Th. M. Rassias and P. Semrl, ? On the behavior of mappings which do not satisfy Hyers-Ulam stability, Proceedings of the American Mathematical Society, 114, pp. 989-993, (1992).
[25] Th. M. Rassias, and J. Tabor, Stability of Mappings of Hyers-Ulam Type, Hardronic Press, (1994).
[26] J. M. Rassias, On the Ulam stability of mixed type mappings on restricted domains, Journal of Mathematical Analysis and Applications, 276, pp. 747-762, (2002).
[27] F. Skof, Local properties and approximations of operators, Rendiconti del Seminario Matematico e Fisico di Milano, 53, pp. 113-129, (1983).
[28] H. Stetkær, Functional equations involving means of functions on the complex plane, Aequationes Mathematicae, 56, pp. 47-62, (1998).
[29] S. M. Ulam, A Collection of Mathematical Problems, Interscience Publishers, 8(1960)
Published
2017-03-23
How to Cite
[1]
H. Dimou, Y. Aribou, A. Chahbi, and S. Kabbaj, “Stability of generalized Jensen functional equation on a set of measure zero”, Proyecciones (Antofagasta, On line), vol. 35, no. 4, pp. 457-468, Mar. 2017.
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