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In this paper, we investigate the generalized Hyers-Ulam stability of the quadratic and quartic type functional equations $$f(kx+y)+f(kx-y)-k^2f(x+y)-k^2f(x-y)-2f(kx)\\{\hfill{67}}+2k^2f(x)+2(k^2-1)f(y)=0,\\f(x+5y)-5f(x+4y)+10f(x+3y)-10f(x+2y)+5f(x+y)\\{\hfill{67}}-f(-x)=0,\\f(kx+y)+f(kx-y)-k^2f(x+y)-k^2f(x-y)\\{\hfill{67}}-{\frac{k^2(k^2-1)}{6}}[f(2x)-4f(x)]+2(k^2-1)f(y)=0$$ by using the fixed point theory in the sense of L. $C{\breve{a}}dariu$ and V. Radu.
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참고문헌 (16)
참고문헌 신청
S. Abbaszadeh / 2010 / Intuitionistic fuzzy stability of a quadratic and quartic func-tional equation / Int. J. Nonlinear Anal. Appl 1:100~124
J. Baker / 2005 / A general functional equation and its stability / Proc. Natl. Acad. Sci 133(6):1657~1664
L. Cădariu / 2003 / Fixed points and the stability of quadratic functional equations / An. Univ. Timisoara Ser. Mat.-Inform 41:25~48
L. Cădariu / 2004 / Iteration Theory / Karl-Franzens-Universitäet :43~52
J. B. Diaz / 1968 / A fixed point theorem of the alternative for con-tractions on a generalized complete metric space / Bull. Amer. Math. Soc 74:305~309
J. Baker / 2005 / A general functional equation and its stability / Proc. Natl. Acad. Sci 133(6):1657~1664
L. Cădariu / 2003 / Fixed points and the stability of quadratic functional equations / An. Univ. Timisoara Ser. Mat.-Inform 41:25~48
L. Cădariu / 2004 / Iteration Theory / Karl-Franzens-Universitäet :43~52
J. B. Diaz / 1968 / A fixed point theorem of the alternative for con-tractions on a generalized complete metric space / Bull. Amer. Math. Soc 74:305~309
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