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December 2016 Ulam-Hyers stability of undecic functional equation in quasi-$\beta$-normed spaces: Fixed point method
K. Ravi, J.M. Rassias, B.V. Senthil Kumar
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Tbilisi Math. J. 9(2): 83-103 (December 2016). DOI: 10.1515/tmj-2016-0022

Abstract

In this paper, we acquire the general solution of the undecic functional equation $$\begin{align*} & f(x+6y)-11f(x+5y)+55f(x+4y)-165f(x+3y)+330f(x+2y)\\ & \qquad\qquad -462f(x+y)+462f(x)-330f(x-y)+165f(x-2y)-55f(x-3y)\\ & \quad\qquad\qquad\qquad\qquad\qquad +11f(x-4y)-f(x-5y)=39916800f(y). \end{align*}$$ We also obtain the generalized Ulam-Hyers stability of the above functional equation in quasi-$\beta$-normed spaces using fixed point method. Moreover, we investigate the pertinent stabilities of the above functional equation using sum of powers of norms, product of powers of norms and mixed product-sum of powers of norms as upper bounds. We also present a counter-example for non-stability of the above functional equation in singular case.

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K. Ravi. J.M. Rassias. B.V. Senthil Kumar. "Ulam-Hyers stability of undecic functional equation in quasi-$\beta$-normed spaces: Fixed point method." Tbilisi Math. J. 9 (2) 83 - 103, December 2016. https://doi.org/10.1515/tmj-2016-0022

Information

Received: 2 May 2015; Accepted: 3 October 2016; Published: December 2016
First available in Project Euclid: 12 June 2018

zbMATH: 1352.39024
MathSciNet: MR3574951
Digital Object Identifier: 10.1515/tmj-2016-0022

Subjects:
Primary: 39B82
Secondary: 39B72

Rights: Copyright © 2016 Tbilisi Centre for Mathematical Sciences

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Vol.9 • No. 2 • December 2016
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