References
- J. Aczél, Lectures on Functional Equations and Their Applications, Academic Press, New York, 1966.
- T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan, 2 (1950), 64–66.
- R. Balasubramanian, Functional inequalities for the quotients of hypergeometric functions, J. Math. Anal. Appl. 218 (1998), 256–268.
- G. Bettencourta and S. Mendes, On the stability of a quadratic functional equation over non-Archimedean spaces, Filomat, 35 (8) (2021), 2693–2704.
- M. Duerinckx and A. Gloria, Multiscale functional inequalities in probability: Concentration properties, ALEA, Lat. Am. J. Probab. Math. Stat. 17 (2020), 133–157.
- A. Ebadian, S. Zolfaghari, S. Ostadbashi and C. Park, Approximation on the reciprocal functional equation in several variables in matrix non-Archimedean random normed spaces, Adv. Difference Equ. 2015 (2015), Article ID 314, 13 pages.
- W. Fechner, Stability of a functional inequality associated with the Jordan-Von Neumann functional equation, Aequationes Math. 71 (2006), 149–161.
- P. Gǎvruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mapppings, J. Math. Anal. Appl. 184 (1994), 431–436.
- M. B. Ghaemi, H. Majani and M.E. Gordji, General system of cubic functional equations in nonArchimedean spaces, Tamsui Oxford J. Inf. Math. Sci. 28(4) (2012) 407–423.
- A. Gilányi, Eine zur Parallelogrammgleichung äquivalente Ungleichung, Aequationes Math. 62 (2001), 303–309.
- A. Gilányi, On a problem by K. Nikodem, Math. Inequal. Appl. 5 (2002), 707–810.
- D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222–224.
- J. L. W. V. Jensen, Sur les fonctions convexes et les inegalities entre les valeurs myennes, Acta Math. 30 (1906), 179–193.
- H. Kawabi, Functional inequalities and an application for parabolic stochastic partial differential equations containing rotation, Bull. Sci. Math. 128 (2004) 687–725.
- M.S. Moslehian and G. Sadeghi, A Mazur-Ulam theorem in non-Archimedean normed spaces, Nonlinear Anal.–TMA 69 (2008), 3405–3408.
- C. Park, Quadratic ρ-functional inequalities and equations, J. Nonlinear Anal. Appl. 2014 (2014) 1–9.
- C. Park, Additive ρ-functional inequalities and equations, J. Math. Inequal. 9 (2015), 17–26.
- C. Park, Additive ρ-functional inequalities in non-Archimedean normed spaces, J. Math. Inequal. 9(2) (2015), 397–407.
- C. Park, Additve ρ-functional inequalities and equations, J. Math. Inequal. 9 (1) (2015), 17–26.
- C. Park, Y. Cho and M. Han, Functional inequalities associated with Jordan-von Neumann-type additive functional equations, J. Inequal. Appl. 2007 (2007), Article ID 41820, 13 pages.
- C. Park, J.R. Lee and D.Y. Shin, Cubic ρ-functional inequality and quartic ρ-functional inequality, J. Comp. Anal. Appl. 21 (2) (2016), 355–362.
- T. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297–300.
- Rätz, On inequalities associated with the Jordan-von Neumann functional equation, Aequationes Math. 66 (2003), 191–200.
- K. Ravi and B. V. Senthil Kumar, Ulam-Gavruta-Rassias stability of Rassias reciprocal functional equation, Global J. Appl. Math. Sci. 3 (1–2) (2010), 57–79.
- K. Ravi and B.V. Senthil Kumar, Stability and geometrical interpretation of reciprocal functional equation, Asian J. Current Engg. Maths, 1(5) (2012), 300–304.
- M. L. Scutaru, S. Vlase, M. Marin and A. Modrea, New analytical method based on dynamic response of planar mechanical elastic systems, Boundary Value Problems, 2020 (104), (2020), 1–16.
- B.V. Senthil Kumar and A. Bodaghi, Approximation of the Jensen type rational functional equation by a fixed point technique, Boletim da Sociedade Paranaense de Matematica, 38(3) (2020), 125–132.
- B. V. Senthil Kumar and H. Dutta, Non-Archimedean stability of a generalized reciprocal-quadratic functional equation in several variables by direct and fixed point methods, Filomat, 32 (9) (2018), 3199–3209.
- W. Suriyacharoen and W. Sintunavarat, On additive ρ-functional equations arising from Cauchy-Jensen functional equations and their stability, Appl. Math. Inf. Sci. 16 (2) (2022), 277–285.
- S. M. Ulam, A Collection of Mathematical Problems, Interscience Publishers, Inc. New York, 1960.
- C. L. Wang, A functional inequality and its applications, J. Math. Anal. Appl. 166 (1992), 247–262.
- Z. Wang, C. Park and D.Y. Shin, Additive ρ-functional inequalities in non-Archimedean 2-normed spaces, AIMS Mathematics, 6 (2) (2020), 1905–1919.