Some results on the stability of bi-exponential functional equations over b-metric spaces

Article Sidebar

PDF
Published: Mar 14, 2018

Main Article Content

Nehjamang Haokip
Gauhati University

Abstract

In this paper, we introduce a bi-exponential function defined on an algebra over the complex field $\mathbb{C}$ which is also a b-metric space. Different results on stability and superstabiltiy of such functional equation are also discussed here with suitable examples.

Downloads

Download data is not yet available.

Article Details

How to Cite
Haokip, N. (2018). Some results on the stability of bi-exponential functional equations over b-metric spaces. Journal of Global Research in Mathematical Archives(JGRMA), 5(3), 106–112. Retrieved from https://www.jgrma.com/index.php/jgrma/article/view/417
Issue
Vol. 5 No. 3 (2018): March-2018
Section
Research Paper

Open Access: This is an open-access journal. All articles published in the Journal of Global Research in Mathematical Archives(JGRMA) are made immediately and permanently available under the Creative Commons Attribution 4.0 International (CC BY 4.0) License. Authors retain the copyright of their work and grant Journal of Global Research in Mathematical Archives(JGRMA)  the right of first publication. This license permits unrestricted use, distribution, adaptation, and reproduction in any medium or format, including commercial use, provided the original author(s), source, and license are properly acknowledged.

Google Scholar Indexed | DOI Enabled | OAI-PMH Compliant | Open Access Journal

References

D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27 (1941),222 - 224.

T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan, Vol. 2, Nos. 1 - 2, Sept., 1950, 64 - 66.

T M Rassias, On the stability of the linear mappings in Banach spaces, Proc. Amer. Math. Soc. Vol. 72, No. 2, November 1978, pp. 297-300.

J. Baker, J. Lawrence and F. Zorzitto, The stability of the equation $f(x+y)=f(x)f(y)$, Proc. Amer. Math. Soc. 74(1979), 242-246.

J. A. Baker, The stability of the cosine equation, Proc. Amer. Math. Soc. 80(1980), 411-416.

S. Czerwik, Contraction mappings in b-metric spaces, Acta. Math. Inform. Univ. Ostra. 1993, 1, 5 - 11.

M. Boriceanu, Fixed point theory for multivalued generalized contraction on a set with two b-metric, studia, univ Babes, Bolya: Math, Liv(3) (2009), 1 - 14.

A. Zivari-Kazempour, Z. Fallah, On the stability of almost bi-multiplicative functionals, Int. J. Pure and Applied Math., Vol. 113, No. 5 (2017), 575-581. doi: 10.12732/ijpam.v113i5.5

J. R. Roshan, V. Parvaneh, S. Sedghi, N. Shobkolaei, W. Shatanawi, Common fixed points of almost generalized $(psi ,varphi)_s$-contractive mappings in ordered b-metric spaces,

Fixed Point Theory and Applications, 2013, (2013):159, doi:10.1186/1687-1812-2013-159.