Stability of mixed type functional equation in normed spaces using fuzzy concept. Issue 5 (4th July 2019)

• Record Type: Journal Article
• Authors: Narasimman, Pasupathi; Dutta, Hemen; Jebril, Iqbal H.
• Is Part Of: International journal of general systems. Volume 48:Issue 5(2019)
• Page Start: 507
• Page End: 522
• Publication Date: 2019-07-04
• Subjects: Additive and quadratic functional equations -- generalized Hyers-Ulam-Rassias stability -- fuzzy normed space; System theory -- Periodicals; 003
• DOI: 10.1080/03081079.2019.1586683
• Languages: English
• ISSNs: 0308-1079

Abstract

ABSTRACT: S. M. Ulam once addressed the problem 'when is it true that a mathematical object satisfying a certain property approximately must be close to an object satisfying the property exactly?'. This problem was solved by D. H. Hyers in 1941 using the functional equation and thereafter numerous research papers and monographs have been published for various types of functional equations in different spaces. The solution proposed by D. H. Hyers (1941) later developed into the famous generalized Hyers-Ulam-Rassias stability of functional equations. In this paper, we intend to attain the general solution to a new mixed type functional equation and interrogate the generalized Hyers–Ulam–Rassias stability in fuzzy normed spaces. Also, we seek to provide its application for generating secret keys in client–server environment.