On the stability of a mean value type functional equation

• Autorzy: Jung S. , Sahoo P.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we prove the stability results of a mean value type functional equation, namely f (x) - g{y) = (x - y)h(x 4- y) which arises from the mean value theorem.

Słowa kluczowe

EN

functional equations; Banach space

PL

równania funkcjonalne; przestrzeń Banacha

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2000
• Tom: Vol. 33, nr 4
• Strony: 793--796
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Jung S.

• Mathematics Section, College of Science & Technology, Hong-Ik University, 339-800 Chochiwon, Korea

autor

Sahoo P.

• Department of Mathematics, University of Louisville, Louisville, KY 40292, U.S.A.

• Mathematics Sections College of Science and Technology Hong-IK University 339-800, ChoChiwon, Korea,

Bibliografia

• [1] J. Aczél, A mean value property of the derivative of quadratic polynomials – without mean values and derivatives, Math. Mag. 58 (1985), 42-45.
• [2] G. L. Forti, Hyers-Ulam stability of functional equations in several variables, Aequationes Math. 50 (1995), 143-190.
• [3] Sh. Haruki, A property of quadratic polynomials, Amer. Math. Monthly 86 (1979), 577-579.
• [4] D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U. S. A. 27 (1941), 222-224.
• [5] D. H. Hyers, G. Isac and Th. M. Rassias, Stability of Functional Equations in Several Variables, Birkhàuser, Boston-Basel-Berlin, 1998.
• [6] D. H. Hyers and Th. M. Rassias, Approximate homomorphisms, Aequationes Math. 44 (1992), 125-153.
• [7] S.-M. Jung, Hyers-Ulam-Rassias stability of functional equations, Dynam. Sys. Appi. 6 (1997), 541-566.
• [8] PI. Kannappan, P. K. Sahoo and M. S. Jacobson, A characterization of low degree polynomials, Demonstratio Math. 28 (1995), 87-96.
• [9] Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.
• [10] P. K. Sahoo and T. Riedel, Mean Value Theorems and Functional Equations, World Scientific, Singapore-New Jersey-London-Hong Kong, 1998.
• [11] S. M. Ulam, Problems in Modern Mathematics, Chap. VI, Wiley, New York, 1960.