Geodesic
Hyers-Ulam--Rassias stability of Pexiderized Cauchy functional equation in 2-Banach spaces
Zamani Eskandani, G.1 ; Gavruta, P.2
1 Faculty of Mathematical Science, University of Tabriz, Tabriz, Iran
2 Department of Mathematics, University Politehnica of Timisoara, Piata Victoriei No. 2, 300006 Timisoara, Romania
Journal of nonlinear sciences and its applications, Tome 5 (2012) no. 6, p. 459-465.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this paper, we investigate stability of the Pexiderized Cauchy functional equation in 2-Banach spaces and pose an open problem.
DOI : 10.22436/jnsa.005.06.06
Classification : 46BXX, 39B72, 47Jxx
Keywords: Linear 2-normed space, Generalized Hyers-Ulam stability, Pexiderized Cauchy functional equation .

Zamani Eskandani, G. 1 ; Gavruta, P. 2

1 Faculty of Mathematical Science, University of Tabriz, Tabriz, Iran
2 Department of Mathematics, University Politehnica of Timisoara, Piata Victoriei No. 2, 300006 Timisoara, Romania 
@article{JNSA_2012_5_6_a5,
     author = {Zamani Eskandani, G. and Gavruta, P.},
     title = {Hyers-Ulam--Rassias stability of {Pexiderized} {Cauchy} functional equation in {2-Banach} spaces},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {459-465},
     publisher = {mathdoc},
     volume = {5},
     number = {6},
     year = {2012},
     doi = {10.22436/jnsa.005.06.06},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.005.06.06/}
}
TY  - JOUR
AU  - Zamani Eskandani, G.
AU  - Gavruta, P.
TI  - Hyers-Ulam--Rassias stability of Pexiderized Cauchy functional equation in 2-Banach spaces
JO  - Journal of nonlinear sciences and its applications
PY  - 2012
SP  - 459
EP  - 465
VL  - 5
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.005.06.06/
DO  - 10.22436/jnsa.005.06.06
LA  - en
ID  - JNSA_2012_5_6_a5
ER  - 
%0 Journal Article
%A Zamani Eskandani, G.
%A Gavruta, P.
%T Hyers-Ulam--Rassias stability of Pexiderized Cauchy functional equation in 2-Banach spaces
%J Journal of nonlinear sciences and its applications
%D 2012
%P 459-465
%V 5
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.005.06.06/
%R 10.22436/jnsa.005.06.06
%G en
%F JNSA_2012_5_6_a5
Zamani Eskandani, G.; Gavruta, P. Hyers-Ulam--Rassias stability of Pexiderized Cauchy functional equation in 2-Banach spaces. Journal of nonlinear sciences and its applications, Tome 5 (2012) no. 6, p. 459-465. doi : 10.22436/jnsa.005.06.06. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.005.06.06/

[1] Aoki, T. On the stability of the linear transformation in Banach spaces, J. Math. Soc. , Volume 2 (1950), pp. 64-66

[2] Aczél, J.; Dhombres, J. Functional Equations in Several Variables, Cambridge University Press, , 1989

[3] Benyamini, Y.; Lindenstrauss, J. Geometric Nonlinear Functional Analysis, vol. 1, Colloq. Publ., vol. 48, Amer. Math. Soc., Providence, RI, 2000

[4] Czerwik, S. Functional Equations and Inequalities in Several Variables, World Scientific, New Jersey, London, Singapore, Hong Kong, 2002

[5] Eskandani, G. Z. On the Hyers-Ulam-Rassias stability of an additive functional equation in quasi-Banach spaces, J. Math. Anal. Appl. , Volume 345 (2008), pp. 405-409

[6] Eskandani, G. Z.; Gavruta, P.; Rassias, J. M.; Zarghami, R. Generalized Hyers-Ulam stability for a general mixed functional equation in quasi-\(\beta\)-normed spaces, Mediterr. J. Math. , Volume 8 (2011), pp. 331-348

[7] Eskandani, G. Z.; Vaezi, H.; Dehghan, Y. N. Stability of mixed additive and quadratic functional equation in non-Archimedean Banach modules, Taiwanese J. Math. , Volume 14 (2010), pp. 1309-1324

[8] Ghler, S. 2-metrische Rume und ihre topologische Struktur, Math. Nachr., Volume 26 (1963), pp. 115-148

[9] Ghler, S. Lineare 2-normierte Rumen, Math. Nachr. , Volume 28 (1964), pp. 1-43

[10] Găvruţa, L.; Găvruţa, P.; Eskandani, G. Z. Hyers-Ulam stability of frames in Hilbert spaces , Bul. Stiint. Univ. Politeh. Timis. Ser. Mat. Fiz., Volume 55(69), 2 (2010), pp. 60-77

[11] Găvruţa, P. On a problem of G. Isac and Th. M. Rassias concerning the stability of mappings, J. Math. Anal. Appl. , Volume 261 (2001), pp. 543-553

[12] Găvruţa, P. An answer to question of John M. Rassias concerning the stability of Cauchy equation, Advanced in Equation and Inequality (1999), pp. 67-71

[13] P. Găvruţa A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. , Volume 184 (1994), pp. 431-436

[14] Hyers, D. H. On the stability of the linear functional equation, Proc. Nat. Acad. Sci. , Volume 27 (1941), pp. 222-224

[15] Hyers, D. H.; Isac, G.; Rassias, Th. M. Stability of Functional Equations in Several Variables, Birkhäuser, Basel, 1998

[16] Jung, S. M. Hyers-Ulam-Rassias Stability of Functional Equations in Mathimatical Analysis, Hadronic Press, Palm Harbor, 2001

[17] Jung, S. M. Asymptotic properties of isometries, J. Math. Anal. Appl. , Volume 276 (2002), pp. 642-653

[18] Kannappan, Pl. Quadratic functional equation and inner product spaces, Results Math., Volume 27 (1995), pp. 368-372

[19] Najati, A.; Eskandani, G. Z. Stability of a mixed additive and cubic functional equation in quasi-Banach spaces, J. Math. Anal. Appl. , Volume 342 (2008), pp. 1318-1331

[20] Park, C. Homomorphisms between Poisson \(JC^*\)-algebras, Bull. Braz. Math. Soc. , Volume 36 (2005), pp. 79-97

[21] Park, W. G. Approximate additive mappings in 2-Banach spaces and related topics, J. Math. Anal. Appl. , Volume 376 (2011), pp. 193-202

[22] Rassias, J. M. On approximation of approximately linear mappings by linear mappings, Journal of Functional Analysis, Volume 46 (1982), pp. 126-130

[23] Rassias, J. M. On approximation of approximately linear mappings by linear mappings, Bulletin des Sciences Mathematiques, Volume 108 (1984), pp. 445-446

[24] Rassias, Th. M. On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. , Volume 72 (1978), pp. 297-300

[25] Th. M. Rassias On a modified Hyers-Ulam sequence, J. Math. Anal. Appl. , Volume 158 (1991), pp. 106-113

[26] Rassias, Th. M. On the stability of functional equations in Banach spaces, J. Math. Anal. Appl. , Volume 251 (2000), pp. 264-284

[27] Th. M. Rassias On the stability of functional equations and a problem of Ulam, Acta Appl. Math., Volume 62 (1) (2000), pp. 23-130

[28] Rassias, Th. M.; Šemrl, P. On the behaviour of mappings which do not satisfy HyersUlam stability, Proc. Amer. Math. Soc. , Volume 114 (1992), pp. 989-993

[29] Rassias, Th. M.; Tabor, J. What is left of Hyers-Ulam stability?, J. Natural Geometry, Volume 1 (1992), pp. 65-69

[30] Ravi, K.; Arunkumar, M.; Rassias, J. M. Ulam stability for the orthogonally general Euler-Lagrange type functional equation, Intern. J. Math. Stat., Volume 3 (A08) (2008), pp. 36-46

[31] Rolewicz, S. Metric Linear Spaces, PWN-Polish Sci. Publ., Warszawa, Reidel, Dordrecht, 1984

[32] Saadati, R.; Cho, Y. J.; Vahidi, J. The stability of the quartic functional equation in various spaces, Comput. Math. Appl. , doi:10.1016/j.camwa.2010.07.034. , 2010

[33] Saadati, R.; Vaezpour, S. M.; Cho, Y. A note on the On the stability of cubic mappings and quadratic mappings in random normed spaces, J. Inequal. Appl., Article ID 214530., 2009

[34] Ulam, S. M. A Collection of the Mathematical Problems , Interscience Publ. New York (1960), pp. 431-436

Cité par Sources :