Abstract
In this chapter, we investigate the stabilities of multiplicative inverse quadratic difference and multiplicative inverse quadratic adjoint functional equations in the setting of non-Archimedean fields via fixed point method.
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References
T. Aoki, On the stability of the linear transformation in Banach spaces. J. Math. Soc. Jpn. 2, 64–66 (1950)
L. Cădariu, V. Radu, Fixed points and the stability of Jensen’s functional equation. J. Inequ. Pure Appl. Math. 4(1), Art. 4 (2003)
L. Cădariu, V. Radu, On the stability of the Cauchy functional equation: a fixed point approach. Grazer Math. Ber. 346, 43–52 (2006)
P. Găvruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings. J. Math. Anal. Appl. 184, 431–436 (1994)
D.H. Hyers, On the stability of the linear functional equation. Proc. Natl. Acad. Sci. USA 27, 222–224 (1941)
S.M. Jung, A fixed point approach to the stability of the equation \(f(x+y)=\frac {f(x)f(y)}{f(x)+f(y)}\). Aust. J. Math. Anal. Appl. 6(1), Art. 8, 1–6 (1998)
B. Margolis, J. Diaz, A fixed point theorem of the alternative for contractions on a generalized complete metric space. Bull. Am. Math. Soc. 74, 305–309 (1968)
A.K. Mirmostafaee, Non-Archimedean stability of quadratic equations. Fixed Point Theory 11(1), 67–75 (2010)
V. Radu, The fixed point alternative and the stability of functional equations. Fixed Point Theory 4(1), 91–96 (2003)
T.M. Rassias, On the stability of the linear mapping in Banach spaces. Proc. Am. Math. Soc. 72, 297–300 (1978)
J.M. Rassias, On approximation of approximately linear mappings by linear mappings. J. Funct. Anal. 46, 126–130 (1982)
K. Ravi, S. Suresh, Solution and generalized Hyers–Ulam stability of a reciprocal quadratic functional equation. Int. J. Pure Appl. Math. 117(2), Art. No. AP2017-31-4927 (2017)
K. Ravi, J.M. Rassias, B.V. Senthil Kumar, A fixed point approach to the generalized Hyers–Ulam stability of reciprocal difference and adjoint functional equations. Thai J. Math. 8(3), 469–481 (2010)
B.V. Senthil Kumar, A. Bodaghi, Approximation of Jensen type reciprocal functional equation using fixed point technique. Boletim da Sociedade Paranaense de Mat. 38(3) (2018). https://doi.org/10.5269/bspm.v38i3.36992
S.M. Ulam, Problems in Modern Mathematics. Chapter VI (Wiley-Interscience, New York, 1964)
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Kumar, B.V.S., Sabarinathan, S., Rassias, M.J. (2019). Stabilities of MIQD and MIQA Functional Equations via Fixed Point Technique. In: Anastassiou, G., Rassias, J. (eds) Frontiers in Functional Equations and Analytic Inequalities. Springer, Cham. https://doi.org/10.1007/978-3-030-28950-8_8
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DOI: https://doi.org/10.1007/978-3-030-28950-8_8
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