Solution and stability of a reciprocal type functional equation in several variables
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Authors
K. Ravi
- PG & Research Department of Mathematics, Sacred Heart College, Tirupattur - 635 601, TamilNadu, India.
E. Thandapani
- Ramanujan Institute of Advance Study in Mathematics, University of Madras, Chepauk, Chennai- 600 005, Tamil Nadu, India.
B.V. Senthil Kumar
- Department of Mathematics, C. Abdul Hakeem College of Engg. and Tech., Melvisharam - 632 509, TamilNadu, India.
Abstract
In this paper, we obtain the general solution and investigate the generalized Hyers-Ulam stability of a
reciprocal type functional equation in several variables of the form
\[\frac{\Pi^m_{ i=2} r(x_1 + x_i)}{\sum ^m_{i=2}[\Pi^m_{ j=2, j\neq i} r(x_1+x_j)]}=\frac{\Pi ^m _{i=1} r(x_i)}{\sum ^m_{i=2}r(x_1)[\Pi^m_{ j=2, j\neq i} r(x_j)]+ (m - 1)\Pi^m_{ i=2} r(x_i)}\]
where \(m\) is a positive integer with \(m \geq 3\).
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ISRP Style
K. Ravi, E. Thandapani, B.V. Senthil Kumar, Solution and stability of a reciprocal type functional equation in several variables, Journal of Nonlinear Sciences and Applications, 7 (2014), no. 1, 18--27
AMA Style
Ravi K., Thandapani E., Kumar B.V. Senthil, Solution and stability of a reciprocal type functional equation in several variables. J. Nonlinear Sci. Appl. (2014); 7(1):18--27
Chicago/Turabian Style
Ravi, K., Thandapani, E., Kumar, B.V. Senthil. "Solution and stability of a reciprocal type functional equation in several variables." Journal of Nonlinear Sciences and Applications, 7, no. 1 (2014): 18--27
Keywords
- Rassias reciprocal functional equation
- General reciprocal functional equations
- Adjoint and difference functional equations
MSC
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