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In this paper, we study two functional equations with two unknown functions from an Abelian group into a commutative ring without zero divisors. The two equations are generalizations of Swiatak's functional equations with an involution. We determine the general solutions of the two functional equations and the properties of the general solutions of the two functional equations under three different hypotheses, respectively. For one of the functional equations, we establish the Hyers-Ulam stability in the case that the unknown functions are complex valued.
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참고문헌 (21)
참고문헌 신청
T. Aoki / 1950 / On the stability of the linear transformation in Banach spaces / J. Math. Soc. Japan 2:64~66
B. Belaid / 2007 / On the generalized Hyers-Ulam stability of Swiatak's functional equation / J. Math. Inequal 1(2):291~300
B. Belaid / 2007 / On the generalized Hyers-Ulam stability of the quadratic functional equation with a general involution / Nonlinear Funct. Anal. Appl 12(2):247~262
N. Brillouet-Belluot / 2012 / On some recent developments in Ulam's type stability / Abstr. Appl. Anal 2012:41
J. K. Chung / 1995 / On a quadratic-trigonometric functional equation and some applications / Trans. Amer. Math. Soc (4):1131~1161
B. Belaid / 2007 / On the generalized Hyers-Ulam stability of Swiatak's functional equation / J. Math. Inequal 1(2):291~300
B. Belaid / 2007 / On the generalized Hyers-Ulam stability of the quadratic functional equation with a general involution / Nonlinear Funct. Anal. Appl 12(2):247~262
N. Brillouet-Belluot / 2012 / On some recent developments in Ulam's type stability / Abstr. Appl. Anal 2012:41
J. K. Chung / 1995 / On a quadratic-trigonometric functional equation and some applications / Trans. Amer. Math. Soc (4):1131~1161
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