Otwarty dostęp

On the Stability of the Functional Equation f(2x+y)+f(x+y2)=2f(x)f(y)f(x)+f(y)+2f(x+y)f(y-x)3f(y-x)-f(x+y)f\left( {2x + y} \right) + f\left( {{{x + y} \over 2}} \right) = {{2f\left( x \right)f\left( y \right)} \over {f\left( x \right) + f\left( y \right)}} + {{2f\left( {x + y} \right)f\left( {y - x} \right)} \over {3f\left( {y - x} \right) - f\left( {x + y} \right)}}

   | 04 lis 2020
Tatra Mountains Mathematical Publications's Cover Image
Tatra Mountains Mathematical Publications
Real Functions, Dynamical Systems and their Applications

Zacytuj

[1] AOKI. T.: On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan 2 (1950), 64–66.10.2969/jmsj/00210064Search in Google Scholar

[2] BOUIKHALENE, B.—ELQUORACHI, E.: Ulam-Găvruta-Rassias stability of the Pexider functional equation, Int. J. Appl. Math. Stat. 7 (2007), no. Fe 07, 27–39.Search in Google Scholar

[3] BOURGIN, D. G.: Class of transformations and bordering transformations, Bull. Amer. Math. Soc. 57 (1951), 223–237.10.1090/S0002-9904-1951-09511-7Search in Google Scholar

[4] BOURGIN, D. G.: Multiplicative transformations, Proc. Nat. Academy Sci. U.S.A. 36(1950), 564–570.10.1073/pnas.36.10.564Search in Google Scholar

[5] CHANG, I. S.—KIM, H. M.: On the Hyers-Ulam stability of quadratic functional equations, J. Ineq. Appl. Math. 33 (2002), 1–12.10.7153/mia-06-08Search in Google Scholar

[6] CHANG, I. S.—JUNG, Y. S.: Stability of functional equations deriving from cubic and quadratic functions, J. Math. Anal. Appl. 283 (2003), 491–500.10.1016/S0022-247X(03)00276-2Search in Google Scholar

[7] CHOLEWA, P. W.: Remarks on the stability of functional equations, Aequationes Math. 27 (1984), 76–86.10.1007/BF02192660Search in Google Scholar

[8] CZERWIK, S.: Functional Equations and Inequalities in Several Variables. World Scientific Publishing Company, New Jersey, London, Singapore and Hong Kong, 2002.10.1142/4875Search in Google Scholar

[9] ESHAGHI GORDJI, M.—ZOLFAGHARI, S.—RASSIAS, J. M.—SAVADKOUHI,M.B.: Solution and stability of amixed type cubic and quartic functional equation in quasi-Banach spaces, Abst. Appl. Anal. 1 (2009), Art. ID 417473, 1–14.10.1155/2009/417473Search in Google Scholar

[10] GHOBADIPOUR, N.—PARK, C.: Cubic-quartic functional equations in fuzzy normed spaces, Int. J. Nonlinear Anal. Appl. 1 (2010), 12–21.Search in Google Scholar

[11] GILÁNYI, A.: Eine zur Parallelogrammgleichung äquivalente Ungleichung, Aequationes Math. 62 (2001), 303–309.10.1007/PL00000156Search in Google Scholar

[12] HYERS, D. H.—ISAC, G.—RASSIAS, TH. M.: Stability of Functional Equations in Several Variables. Birkhauser, Basel, 1998.10.1007/978-1-4612-1790-9Search in Google Scholar

[13] HYERS, D. H.: On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27(1941), no. 4, 222–224.10.1073/pnas.27.4.222Search in Google Scholar

[14] JUNG, S.-M.: Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis. In: Springer Optimization and Its Applications Vol. 48. Springer, New York, 2011.10.1007/978-1-4419-9637-4Search in Google Scholar

[15] JUNG, S.-M.—POPA, D.—RASSIAS, M. TH.: On the stability of the linear functional equation in a single variable on complete metric groups, J. Global Optim. 59 (2014), no. 1 165–171.10.1007/s10898-013-0083-9Search in Google Scholar

[16] KANG, D.: On the stability of generalized quartic mappings in quasi-β-normed spaces, J. Inequal. Appl. (2010), Art. ID 198098, 11 pp.10.1155/2010/198098Search in Google Scholar

[17] KANNAPPAN, PL.: Functional Equations and Inequalities with Applications. In: Springer Monographs in Mathematics. Springer, New York, NY, 2009.10.1007/978-0-387-89492-8Search in Google Scholar

[18] RASSIAS, TH. M.: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297–300.10.1090/S0002-9939-1978-0507327-1Search in Google Scholar

[19] PARK, C.—KWON, S. M.,—LEE, J. R.: Hyers-ulam stability of additive function equations in paranormed spaces, J. Comput. Anal. Appl. 26 (2019), no. 3, 532–538.Search in Google Scholar

[20] PARK, C.—BODAGHI, A.: Two multi-cubic functional equations and some results on the stability in modular spaces, J. Inequal. Appl. 2020, Art. no. 6. https://doi.org/10.1186/s13660-019-2274-510.1186/s13660-019-2274-5Search in Google Scholar

[21] PARK, W. G.—BAE, J. H.: A functional equation originating from elliptic curves, Abst. Appl. Anal. 2008, Art. ID. 135237, 10 pp.10.1155/2008/135237Search in Google Scholar

[22] PARK, C.—RASSIAS, M. TH.: Additive functional equations and partial multipliers in C*-algebras, R. Acad. Cienc. Exactas, Fís., Nat. Ser. A. Mat., Revista de la Real Academia de Ciencias Exactas, Serie A. Matemáticas, RACSAM 113 (2019), no. 3, 2261–2275.10.1007/s13398-018-0612-ySearch in Google Scholar

[23] RASSIAS, J. M.: On approximately of approximately linear mappings by linear mappings, J. Funct. Anal. USA. 46 (1982), 126–130.10.1016/0022-1236(82)90048-9Search in Google Scholar

[24] RASSIAS, J. M.: Solution of problem of Ulam, J.Approx. Theory. USA. 57(1989), no. 3, 268–273.10.1016/0021-9045(89)90041-5Search in Google Scholar

[25] RASSIAS, J. M.—ARUNKUMAR, M.—RAMAMOORTHI, S.—HEMALATHA, S.: Ulam-Hyers stability of a 2-variable AC-mixed type functional equation in quasi-β-normed spcaes:direct and fixed point methods. Malaya J. Math. 2 (2014), no. 2, 108–128.Search in Google Scholar

[26] RAVI, K.—RASSIAS, J. M.—SENTHIL KUMAR, B. V.: Ulam stability of reciprocal difference and adjoint funtional equations, Aust. J. Math. Anal. Appl. 8 (2011), no. 1, Art. ID 13, 18 pp. (Erratum ibid. 9, (2012), no. 1, Art. ID. 23, 2 pp.)Search in Google Scholar

[27] RAVI, K.—ARUNKUMAR, M.—RASSIAS, J. M.: Ulam stability for the orthogonally general Euler-Lagrange type functional equation, Int. J. Math. Stat. 3 (2008), no. A 08, 36–46.Search in Google Scholar

[28] RAVI, K.,—SENTHIL KUMAR, B. V.: Ulam-Gavruta-Rassias stability of Rassias reciprocal functional equation, Glob. J. Appl. Math. Math. Sci., Vol. 3 (2010), no. 1–2, 57–79.Search in Google Scholar

[29] RAVI, K.—RASSIAS, J. M.—SENTHIL KUMAR, B. V.: Ulam stability of Generalized Reciprocal Funtional Equation in several variables, Int. J. Appl. Math. Stat. 19 (2010), 1–19.Search in Google Scholar

[30] RAVI, K.—RASSIAS, J. M.—SENTHIL KUMAR, B. V.: Ulam Stability of a generalized reciprocal type functional equation in non-Archimedean fields. Arabian J. Math. 4 (2015), 117–126.10.1007/s40065-014-0121-6Search in Google Scholar

[31] SENTHIL KUMAR, B. V.—RASSIAS, J. M.—RAVI, K.: Ulam stability of a bi-reciprocal functional equation in quasi-β-normed spaces, Novi Sad J. Math. 46 (2016), no. 2, 1–11.10.30755/NSJOM.03219Search in Google Scholar

[32] ULAM, S. M.: A Collection of Mathematical Problems. Interscience, New York, 1960.Search in Google Scholar

eISSN:
1210-3195
Język:
Angielski
Częstotliwość wydawania:
3 razy w roku
Dziedziny czasopisma:
Mathematics, General Mathematics