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In this paper, I prove the stability of the following set-valued functional equation $$f(x+2y){\oplus}f(x-2y){\oplus}3f(2x){\oplus}f(-2x)\\{\hspace{100}}=4f(x+y){\oplus}4f(x-y){\oplus}10f(x)$$ by employing the direct method in the sense of Hyers and Ulam.
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참고문헌 (18)
참고문헌 신청
L. Cadariu / 2003 / Fixed points and the stability of quadratic functional equations / An. Univ. Timisoara Ser. Mat.-Inform 41:25~48
L. Cadariu / 2004 / On the stability of the Cauchy functional equation: a fixed point approach in Iteration Theory / Grazer Mathematische Berichte, Karl-Franzens-Universitaet, Graz, Graz, Austria 346:43~52
C. Castaing / 1977 / Lec. Notes in Math., vol. 580 / Springer
H.Y. Chu / 2014 / On the stability of the generalized cubic set-valued functional equation / Appl. Math. Lett 37:7~14
J. B. Diaz / 1968 / A fixed point theorem of the alternative for contrac-tions on a generalized complete metric space / Bull. Amer. Math. Soc 74:305~309
L. Cadariu / 2004 / On the stability of the Cauchy functional equation: a fixed point approach in Iteration Theory / Grazer Mathematische Berichte, Karl-Franzens-Universitaet, Graz, Graz, Austria 346:43~52
C. Castaing / 1977 / Lec. Notes in Math., vol. 580 / Springer
H.Y. Chu / 2014 / On the stability of the generalized cubic set-valued functional equation / Appl. Math. Lett 37:7~14
J. B. Diaz / 1968 / A fixed point theorem of the alternative for contrac-tions on a generalized complete metric space / Bull. Amer. Math. Soc 74:305~309
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