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In the current work, we define and find the general solution of the decic functional equation g(x + 5y) - 10g(x + 4y) + 45g(x + 3y) - 120g(x + 2y) + 210g(x + y) - 252g(x) + 210g(x - y) - 120g(x - 2y) + 45g(x - 3y) - 10g(x - 4y) + g(x - 5y) = 10!g(y) where 10! = 3628800. We also investigate and establish the generalized Ulam-Hyers stability of this functional equation in Banach spaces, generalized 2-normed spaces and random normed spaces by using direct and fixed point methods.
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참고문헌 (69)
참고문헌 신청
M. AcikgAoz / 2007 / A review on 2-normed structures / Int. J. Math. Anal 1(4):187~191
J. Aczel / 1989 / Functional Equations in Several Variables / Cam-bridge Univ
C. Alsina / 1986 / On the stability of a functional equation arising in probabilistic normed spaces, General Inequal / Oberwolfach 5:263~271
T. Aoki / 1950 / On the stability of the linear transformation in Banach spaces / J. Math. Soc. Japan 2:64~66
M. Arunkumar / 2012 / Ulam-Hyers stability of a 2-variable AC-mixed type functional equation: direct and fixed point methods / J. Mod. Math. Front 1(3):10~26
J. Aczel / 1989 / Functional Equations in Several Variables / Cam-bridge Univ
C. Alsina / 1986 / On the stability of a functional equation arising in probabilistic normed spaces, General Inequal / Oberwolfach 5:263~271
T. Aoki / 1950 / On the stability of the linear transformation in Banach spaces / J. Math. Soc. Japan 2:64~66
M. Arunkumar / 2012 / Ulam-Hyers stability of a 2-variable AC-mixed type functional equation: direct and fixed point methods / J. Mod. Math. Front 1(3):10~26
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