STABILITY OF TREDECIC FUNCTIONAL EQUATION IN MATRIX NORMED SPACES
DOI:
https://doi.org/10.24297/jam.v13i2.5947Keywords:
Hyers-Ulam stability, xed point, tredecic functional equation, matrix normed spacesAbstract
In this current work, we dene and nd the general solution of the tredecic functional equation. We also investigate and establish the generalized Ulam-Hyers stability of this functional equation in matrix normed spaces by using the xed point method.
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References
[1] T. Aoki , On the Stability of the Linear Transformation in Banach Spaces, J. Math. Soc. Japan, 2 (1950), 64-66.
[2] M. Arunkumar, A. Bodaghi, J. M. Rassias and Elumalai Sathiya, The General Solution and Approximations of a Decic Type Functional Equation in Various Normed Spaces, Journal of the
Chungcheong Mathematical Society, 29(2), (2016), 287-328.
[3] L. Cadariu and V. Radu, Fixed Points and the Stability of Jensen's Functional Equation.,J. Inequal. Pure Appl. Math., 4(1) (2003), 1-7.
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[5] D. H. Hyers, On the Stability of the Linear Functional Equation, Proc. Natl. Acad. Sci. USA, 27 (1941), 222-224.
[6] G. Isac and Th. M. Rassias, Stability of ' -Additive Mappings: Applications to Nonlinear Analysis, J. Funct. Anal., 19 (1996), 219-228.
[7] J. Lee, D. Shin and C. Park, An Additive Functional Inequality in Matrix Normed Spaces, Mathematical Inequalities and Applications, 16(4)(2013), 1009-1022.
[8] J. Lee, D. Shin and C. Park, An AQCQ- Functional Equation in Matrix Normed Spaces, Result. Math., 64 2013:146, 1-15.
[9] J. Lee, D. Shin and C. Park, Hyers-Ulam Stability of Functional Equations in Matrix Normed Spaces, Journal of Inequalities and Applications, 2013:22, 1-11.
[10] J. Lee, C. Park and D. Shin, Functional Equations in Matrix Normed Spaces, Proc. Indian Acad. sci., 125(3) (2015), 399-412.
[11] D. Mihet and V. Radu, On the Stability of the Additive Cauchy Functional Equation in Random Normed Spaces, J. Math. Anal. Appl., 343 (2008), 567-572.
[12] R. Murali and V. Vithya, Hyers-Ulam-Rassias Stability of Functional Equations in Matrix Normed Spaces: A xed point approach, Assian Journal of Mathematics and Computer Research, 4(3) (2015),
155-163.
[13] C. Park, Stability of an AQCQ-Functional Equation in Paranormed Spaces, Advances in Dierence Equations., 2012:148, 1-20.
[14] Th. M. Rassias, On the Stability of the Linear Mapping in Banach Spaces, Proc. Am. Math. Soc., 72 (1978), 297-300.
[15] J. M. Rassias and Mohammad Eslamian, Fixed Points and Stability of Nonic Functional Equation in Quasi - Normed Spaces, Contemporary Anal. Appl. Math., 3(2) (2015), 293-309.
[16] K. Ravi, J.M. Rassias and B.V. Senthil Kumar, Ulam-Hyers Stability of Undecic Functional Equation in Quasi- Normed Spaces: Fixed Point Method, Tbilisi Mathematical Science, 9(2) (2016), 83-103.
[17] Y. Shen, W. Chen, On the Stability of Septic and Octic Functional Equations, J. Computational Analysis and Applications, 18(2), (2015), 277-290.
[18] S. M. Ulam, Problems in Modern Mathematics, Science Editions, Wiley, NewYork (1964).
[19] Z.Wang and P. K. Sahoo, Stability of an ACQ- Functional Equation in Various Matrix Normed Spaces, J. Nonlinear Sci. Appl., 8 (2015), 64-85.
[20] T. Z. Xu , J.M. Rassias, M. J. Rassias, and W. X. Xu, A Fixed Point Approach to the Stability of Quintic and Sextic Functional Equations in Quasi- Normed Spaces. Journal of Inequalities and
Applications, (2010), 1-23.
[2] M. Arunkumar, A. Bodaghi, J. M. Rassias and Elumalai Sathiya, The General Solution and Approximations of a Decic Type Functional Equation in Various Normed Spaces, Journal of the
Chungcheong Mathematical Society, 29(2), (2016), 287-328.
[3] L. Cadariu and V. Radu, Fixed Points and the Stability of Jensen's Functional Equation.,J. Inequal. Pure Appl. Math., 4(1) (2003), 1-7.
[4] P. Gavruta, A Generalization of the Hyers-Ulam Rassias Stability of Approximately Additive Mappings, J. Math. Anal. Appl., 184 (1994), 431-436.
[5] D. H. Hyers, On the Stability of the Linear Functional Equation, Proc. Natl. Acad. Sci. USA, 27 (1941), 222-224.
[6] G. Isac and Th. M. Rassias, Stability of ' -Additive Mappings: Applications to Nonlinear Analysis, J. Funct. Anal., 19 (1996), 219-228.
[7] J. Lee, D. Shin and C. Park, An Additive Functional Inequality in Matrix Normed Spaces, Mathematical Inequalities and Applications, 16(4)(2013), 1009-1022.
[8] J. Lee, D. Shin and C. Park, An AQCQ- Functional Equation in Matrix Normed Spaces, Result. Math., 64 2013:146, 1-15.
[9] J. Lee, D. Shin and C. Park, Hyers-Ulam Stability of Functional Equations in Matrix Normed Spaces, Journal of Inequalities and Applications, 2013:22, 1-11.
[10] J. Lee, C. Park and D. Shin, Functional Equations in Matrix Normed Spaces, Proc. Indian Acad. sci., 125(3) (2015), 399-412.
[11] D. Mihet and V. Radu, On the Stability of the Additive Cauchy Functional Equation in Random Normed Spaces, J. Math. Anal. Appl., 343 (2008), 567-572.
[12] R. Murali and V. Vithya, Hyers-Ulam-Rassias Stability of Functional Equations in Matrix Normed Spaces: A xed point approach, Assian Journal of Mathematics and Computer Research, 4(3) (2015),
155-163.
[13] C. Park, Stability of an AQCQ-Functional Equation in Paranormed Spaces, Advances in Dierence Equations., 2012:148, 1-20.
[14] Th. M. Rassias, On the Stability of the Linear Mapping in Banach Spaces, Proc. Am. Math. Soc., 72 (1978), 297-300.
[15] J. M. Rassias and Mohammad Eslamian, Fixed Points and Stability of Nonic Functional Equation in Quasi - Normed Spaces, Contemporary Anal. Appl. Math., 3(2) (2015), 293-309.
[16] K. Ravi, J.M. Rassias and B.V. Senthil Kumar, Ulam-Hyers Stability of Undecic Functional Equation in Quasi- Normed Spaces: Fixed Point Method, Tbilisi Mathematical Science, 9(2) (2016), 83-103.
[17] Y. Shen, W. Chen, On the Stability of Septic and Octic Functional Equations, J. Computational Analysis and Applications, 18(2), (2015), 277-290.
[18] S. M. Ulam, Problems in Modern Mathematics, Science Editions, Wiley, NewYork (1964).
[19] Z.Wang and P. K. Sahoo, Stability of an ACQ- Functional Equation in Various Matrix Normed Spaces, J. Nonlinear Sci. Appl., 8 (2015), 64-85.
[20] T. Z. Xu , J.M. Rassias, M. J. Rassias, and W. X. Xu, A Fixed Point Approach to the Stability of Quintic and Sextic Functional Equations in Quasi- Normed Spaces. Journal of Inequalities and
Applications, (2010), 1-23.
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Published
2017-05-06
How to Cite
Pinelas, S., RAMDOSS, M., & VEERAMANI, V. (2017). STABILITY OF TREDECIC FUNCTIONAL EQUATION IN MATRIX NORMED SPACES. JOURNAL OF ADVANCES IN MATHEMATICS, 13(2), 7135–7146. https://doi.org/10.24297/jam.v13i2.5947
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