Stability of generalized Jensen functional equation on a set of measure zero
DOI:
https://doi.org/10.4067/S071609172016000400007Keywords:
KJensen functional equation, HyersUlam stability, ecuación funcional KJensen, estabilidad de HyersUlamAbstract
Let E is a complex vector space and F is real (or complex ) Banach space. In this paper, we prove the HyersUlam stability for the generalized Jensen functional equation
References
[1] T. Aoki, On the stability of the linear transformation in Banach spaces, Journal of the Mathematical Society of Japan, 2, pp. 6466, (1950).
[2] J. A. Baker, A general functional equation and its stability, Proceeding of the American Mathematical Society, 133, pp. 16571664, (2005).
[3] N. BrillouetBelluot, 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 HyersUlam stability of functional equations on restricted domains, The Australian Journal of Mathematical Analysis and Applications, 6, pp. 110, (2009).
[5] A. B. Chahbi, A. Charifi, B. Bouikhalene and S. Kabbaj, Nonarchimedean stability of a Pexider Kquadratic functional equation, Arab Journal of Mathematical Sciences, 21, pp. 6783, (2015).
[6] A. Chahbi, M. Almahalebi, A. Charifi and S.Kabbaj Generalized Jensen functional equation on restricted domain, Annals of West University of TimisoaraMathematics, 52, pp. 2939, (2014).
[7] P. W. Cholewa, Remarks on the stability of functional equations, Aequationes mathematicae, 27, pp. 7686, (1984).
[8] J. Chung, Stability of a conditional Cauchy equation on a set of measure zero, Aequationes mathematicae, 87, pp. 391400, (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. 10651075, (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. 111, (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. 5964, (1992).
[12] P. Gavruta, A generalization of the HyersUlamRassias stability of approximately additive mappings, Journal of Mathematical Analysis and Applications, 184, pp. 431436, (1994).
[13] D. H. Hyers, On the stability of the linear functional equation, Proceedings of the National Academy of Sciences, 27, pp. 222224, (1941).
[14] D. H. Hyers and Th. M. Rassias, Approximate homomorphisms, Aequationes Mathematicae, 44, pp. 125153, (1992).
[15] D. H. Hyers, Transformations with bounded nth differences, Pacific Journal of Mathematics, 11, pp. 591602, (1961).
[16] K. W. Jun and Y. H. Lee, A generalization of the HyersUlamRassias stability of Jensen0s equation, Journal of Mathematical Analysis and Applications, 238, pp. 305315, (1999).
[17] S. M. Jung, On the HyersUlam stability of the functional equations that have the quadratic property, Journal of Mathematical Analysis and Applications, 222, pp. 126137, (1998).
[18] C. F. K. Jung, On generalized complete metric spaces, Bulletin of the American Mathematical Society, 75, pp. 113116, (1969).
[19] R. Ã Lukasik, Some generalization of Cauchy0s and the quadratic functional equations, Aequationes Mathematicae, 83, pp. 7586, (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, NewYork (1980).
[22] Th. M. Rassias, On the stability of linear mapping in Banach spaces, Proceedings of the American Mathematical Society, 72, pp. 297300, (1978).
[23] Th. M. Rassias, On the stability of the functional equations and a problem of Ulam, Acta Applicandae Mathematicae, 62, pp. 23130, (2000).
[24] Th. M. Rassias and P. Semrl, ? On the behavior of mappings which do not satisfy HyersUlam stability, Proceedings of the American Mathematical Society, 114, pp. 989993, (1992).
[25] Th. M. Rassias, and J. Tabor, Stability of Mappings of HyersUlam 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. 747762, (2002).
[27] F. Skof, Local properties and approximations of operators, Rendiconti del Seminario Matematico e Fisico di Milano, 53, pp. 113129, (1983).
[28] H. Stetkær, Functional equations involving means of functions on the complex plane, Aequationes Mathematicae, 56, pp. 4762, (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. 16571664, (2005).
[3] N. BrillouetBelluot, 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 HyersUlam stability of functional equations on restricted domains, The Australian Journal of Mathematical Analysis and Applications, 6, pp. 110, (2009).
[5] A. B. Chahbi, A. Charifi, B. Bouikhalene and S. Kabbaj, Nonarchimedean stability of a Pexider Kquadratic functional equation, Arab Journal of Mathematical Sciences, 21, pp. 6783, (2015).
[6] A. Chahbi, M. Almahalebi, A. Charifi and S.Kabbaj Generalized Jensen functional equation on restricted domain, Annals of West University of TimisoaraMathematics, 52, pp. 2939, (2014).
[7] P. W. Cholewa, Remarks on the stability of functional equations, Aequationes mathematicae, 27, pp. 7686, (1984).
[8] J. Chung, Stability of a conditional Cauchy equation on a set of measure zero, Aequationes mathematicae, 87, pp. 391400, (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. 10651075, (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. 111, (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. 5964, (1992).
[12] P. Gavruta, A generalization of the HyersUlamRassias stability of approximately additive mappings, Journal of Mathematical Analysis and Applications, 184, pp. 431436, (1994).
[13] D. H. Hyers, On the stability of the linear functional equation, Proceedings of the National Academy of Sciences, 27, pp. 222224, (1941).
[14] D. H. Hyers and Th. M. Rassias, Approximate homomorphisms, Aequationes Mathematicae, 44, pp. 125153, (1992).
[15] D. H. Hyers, Transformations with bounded nth differences, Pacific Journal of Mathematics, 11, pp. 591602, (1961).
[16] K. W. Jun and Y. H. Lee, A generalization of the HyersUlamRassias stability of Jensen0s equation, Journal of Mathematical Analysis and Applications, 238, pp. 305315, (1999).
[17] S. M. Jung, On the HyersUlam stability of the functional equations that have the quadratic property, Journal of Mathematical Analysis and Applications, 222, pp. 126137, (1998).
[18] C. F. K. Jung, On generalized complete metric spaces, Bulletin of the American Mathematical Society, 75, pp. 113116, (1969).
[19] R. Ã Lukasik, Some generalization of Cauchy0s and the quadratic functional equations, Aequationes Mathematicae, 83, pp. 7586, (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, NewYork (1980).
[22] Th. M. Rassias, On the stability of linear mapping in Banach spaces, Proceedings of the American Mathematical Society, 72, pp. 297300, (1978).
[23] Th. M. Rassias, On the stability of the functional equations and a problem of Ulam, Acta Applicandae Mathematicae, 62, pp. 23130, (2000).
[24] Th. M. Rassias and P. Semrl, ? On the behavior of mappings which do not satisfy HyersUlam stability, Proceedings of the American Mathematical Society, 114, pp. 989993, (1992).
[25] Th. M. Rassias, and J. Tabor, Stability of Mappings of HyersUlam 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. 747762, (2002).
[27] F. Skof, Local properties and approximations of operators, Rendiconti del Seminario Matematico e Fisico di Milano, 53, pp. 113129, (1983).
[28] H. Stetkær, Functional equations involving means of functions on the complex plane, Aequationes Mathematicae, 56, pp. 4762, (1998).
[29] S. M. Ulam, A Collection of Mathematical Problems, Interscience Publishers, 8(1960)
Published
20170323
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. 457468, Mar. 2017.
Issue
Section
Artículos

Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
 No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.