Tbilisi Mathematical Journal

Various generalized Ulam-Hyers stabilities of a nonic functional equations

John M. Rassias, M. Arunkumar, E. Sathya, and T. Namachivayam

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Abstract

In this paper, we have established the general solution and generalized Ulam - Hyers stability of the following nonic functional equation \begin{align*} & f(x+5y)-9f(x+4y)+36f(x+3y)-84f(x+2y)+126f(x+y)-126f(x)\\ & \qquad \qquad\qquad\qquad +84f(x-y)-36f(x-2y)+9f(x-3y)-f(x-4y) = 9! f(y) \end{align*} where $9! = 362880$ in a Banach Space ($\textbf{BS}$), Felbin's type Fuzzy Normed Space ($\textbf{FFNS}$) and Intuitionistic Fuzzy Normed Space ($\textbf{IFNS}$) using the standard direct and fixed point method.

Article information

Source
Tbilisi Math. J., Volume 9, Issue 1 (2016), 159-196.

Dates
Received: 2 August 2015
Accepted: 5 January 2016
First available in Project Euclid: 12 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1528769045

Digital Object Identifier
doi:10.1515/tmj-2016-0008

Mathematical Reviews number (MathSciNet)
MR3483660

Zentralblatt MATH identifier
1338.39037

Subjects
Primary: 39B52: Equations for functions with more general domains and/or ranges
Secondary: 32B72 32B82

Keywords
Nonic functional equation generalized Ulam - Hyers stability Banach space Felbin's type fuzzy normed space Intuitionistic fuzzy normed space

Citation

Rassias, John M.; Arunkumar, M.; Sathya, E.; Namachivayam, T. Various generalized Ulam-Hyers stabilities of a nonic functional equations. Tbilisi Math. J. 9 (2016), no. 1, 159--196. doi:10.1515/tmj-2016-0008. https://projecteuclid.org/euclid.tbilisi/1528769045


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