Tbilisi Mathematical Journal

Approximate $n$-dimensional additive functional equation in various Banach spaces

Abasalt Bodaghi, Mohan Arunkumar, and Elumalai Sathya

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Abstract

In this paper, we modify the Cauchy additive functional equation and find all solutions of this new functional equation. Then, we study generalized Ulam-Hyers stability of such functional equation in various Banach spaces via Hyers' method.

Article information

Source
Tbilisi Math. J., Volume 11, Issue 2 (2018), 77-96.

Dates
Received: 30 January 2018
Accepted: 10 March 2018
First available in Project Euclid: 20 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1529460024

Digital Object Identifier
doi:10.32513/tbilisi/1529460024

Mathematical Reviews number (MathSciNet)
MR3954185

Subjects
Primary: 39B52: Equations for functions with more general domains and/or ranges
Secondary: 39B72: Systems of functional equations and inequalities 39B82: Stability, separation, extension, and related topics [See also 46A22]

Keywords
additive functional equations generalized Ulam-Hyers stability Banach space 2-Banach space quasi 2-Banach space Quasi-$beta$-Banach space fuzzy quasi-$beta$-Banach space

Citation

Bodaghi, Abasalt; Arunkumar, Mohan; Sathya, Elumalai. Approximate $n$-dimensional additive functional equation in various Banach spaces. Tbilisi Math. J. 11 (2018), no. 2, 77--96. doi:10.32513/tbilisi/1529460024. https://projecteuclid.org/euclid.tbilisi/1529460024


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