Stabilities of MIQD and MIQA Functional Equations via Fixed Point Technique
Chapter
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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.
References
- 1.T. Aoki, On the stability of the linear transformation in Banach spaces. J. Math. Soc. Jpn. 2, 64–66 (1950)MathSciNetCrossRefGoogle Scholar
- 2.L. Cădariu, V. Radu, Fixed points and the stability of Jensen’s functional equation. J. Inequ. Pure Appl. Math. 4(1), Art. 4 (2003)Google Scholar
- 3.L. Cădariu, V. Radu, On the stability of the Cauchy functional equation: a fixed point approach. Grazer Math. Ber. 346, 43–52 (2006)MathSciNetzbMATHGoogle Scholar
- 4.P. Găvruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings. J. Math. Anal. Appl. 184, 431–436 (1994)MathSciNetCrossRefGoogle Scholar
- 5.D.H. Hyers, On the stability of the linear functional equation. Proc. Natl. Acad. Sci. USA 27, 222–224 (1941)MathSciNetCrossRefGoogle Scholar
- 6.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)Google Scholar
- 7.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)MathSciNetCrossRefGoogle Scholar
- 8.A.K. Mirmostafaee, Non-Archimedean stability of quadratic equations. Fixed Point Theory 11(1), 67–75 (2010)MathSciNetzbMATHGoogle Scholar
- 9.V. Radu, The fixed point alternative and the stability of functional equations. Fixed Point Theory 4(1), 91–96 (2003)MathSciNetzbMATHGoogle Scholar
- 10.T.M. Rassias, On the stability of the linear mapping in Banach spaces. Proc. Am. Math. Soc. 72, 297–300 (1978)MathSciNetCrossRefGoogle Scholar
- 11.J.M. Rassias, On approximation of approximately linear mappings by linear mappings. J. Funct. Anal. 46, 126–130 (1982)MathSciNetCrossRefGoogle Scholar
- 12.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)Google Scholar
- 13.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)MathSciNetzbMATHGoogle Scholar
- 14.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
- 15.S.M. Ulam, Problems in Modern Mathematics. Chapter VI (Wiley-Interscience, New York, 1964)zbMATHGoogle Scholar
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