Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter September 14, 2016

Ulam–Hyers stabilities of a generalized composite functional equation in non-Archimedean spaces

  • Pasupathi Narasimman EMAIL logo and John Michael Rassias

Abstract

In this paper, we introduce a new generalized composite functional equation and prove its Hyers–Ulam–Rassias stability, Ulam–Găvruta–Rassias stability and Ulam–J. Rassias stability in non-Archimedean normed spaces using a fixed point method.

MSC 2010: 39B55; 39B52; 39B82

References

[1] Azadi Kenary H., Non-Archimedean stability of Cauchy–Jensen type functional equation, Int. J. Nonlinear Anal. Appl. 2 (2011), no. 2, 92–102. Search in Google Scholar

[2] Azadi Kenary H., Hyers–Ulam–Rassias stability of a composite functional equation in various normed spaces, Bull. Iranian Math. Soc. 39 (2013), no. 3, 383–403. Search in Google Scholar

[3] Baker J. A., The stability of certain functional equations, Proc. Amer. Math. Soc. 112 (1991), 729–732. 10.1090/S0002-9939-1991-1052568-7Search in Google Scholar

[4] Bodaghi A., Stability of a mixed type additive and quartic function equation, Filomat 28 (2014), no. 8, 1629–1640. 10.2298/FIL1408629BSearch in Google Scholar

[5] Bodaghi A. and Kim S. O., Ulam’s type stability of a functional equation deriving from quadratic and additive functions, J. Math. Inequal. 9 (2015), no. 1, 73–84. 10.7153/jmi-09-07Search in Google Scholar

[6] Bouikhalene B., Elqorachi E. and Rassias J. M., A fixed points approach to stability of the Pexider equation, Tbilisi Math. J. 7 (2014), no. 2, 95–110. 10.2478/tmj-2014-0021Search in Google Scholar

[7] Hyers D. H., On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA 27 (1941), 222–224. 10.1073/pnas.27.4.222Search in Google Scholar

[8] Margolis B. and Diaz J. B., A fixed point theorem of the alternative for contractions on the generalized complete metric space, Bull. Amer. Math. Soc. 74 (1968), 305–309. 10.1090/S0002-9904-1968-11933-0Search in Google Scholar

[9] Mihet D. and Radu V., On the stability of the additive Cauchy functional equation in random normed spaces, J. Math. Anal. Appl. 343 (2008), 567–572. 10.1016/j.jmaa.2008.01.100Search in Google Scholar

[10] Rassias J. M., On approximation of approximately linear mappings by linear mappings, J. Funct. Anal. 46 (1982), 126–130. 10.1016/0022-1236(82)90048-9Search in Google Scholar

[11] Rassias J. M., On approximation of approximately linear mappings by linear mappings, Bull. Sci. Math. 108 (1984), 445–446. 10.1016/0022-1236(82)90048-9Search in Google Scholar

[12] Rassias T. M., On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297–300. 10.1090/S0002-9939-1978-0507327-1Search in Google Scholar

[13] Ravi K., Arunkumar M. and Rassias J. M., On the Ulam stability for an orthogonally general Euler–Lagrange type functional equation, Int. J. Math. Stat. 3 (2008), no. A08, 36–46. Search in Google Scholar

[14] Ravi K. and Narasimman P., Solution and stability of a mixed type functional equation in RN-spaces, Int. J. Sci. Engrg. Res. 3 (2012), no. 11, 16–25. Search in Google Scholar

[15] Ravi K. and Narasimman P., Stability of generalized quadratic functional equation in non-archimedean fuzzy normed spaces, Adv. Mater. Res. 403–408 (2012), 879–887. 10.4028/www.scientific.net/AMR.403-408.879Search in Google Scholar

[16] Ravi K. and Ponmanaselvan A., On a composite functional equation related to abelian Groups, Int. J. Math. Trends Technol. 17 (2015), no. 1, 75–81. 10.14445/22315373/IJMTT-V17P510Search in Google Scholar

[17] Ravi K., Rassias M. J., Narasimman P. and Kumar R. K., Stabilities of a general k-cubic functional equation in Banach spaces, Contemp. Anal. Appl. Math. 3 (2015), no. 1, 1–12. 10.18532/caam.94458Search in Google Scholar

[18] Rassias M. J., J. M. Rassias product-sum stability of an Euler–Lagrange functional equation, J. Nonlinear Sci. Appl. 3 (2010), no. 4, 265–271. 10.22436/jnsa.003.04.05Search in Google Scholar

[19] Ulam S. M., A Collection of the Mathematical Problems, Interscience Publisher, New York, 1960. Search in Google Scholar

Received: 2016-3-11
Revised: 2016-6-24
Accepted: 2016-7-21
Published Online: 2016-9-14
Published in Print: 2016-10-1

© 2016 by De Gruyter

Downloaded on 26.4.2024 from https://www.degruyter.com/document/doi/10.1515/apam-2016-0023/html
Scroll to top button