A Fixed Point Approach to the Stability of the Cauchy Additive and Quadratic Type Functional Equation

نویسندگان

  • Sun Sook Jin
  • Yang-Hi Lee
چکیده

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A fixed point approach to the stability of additive-quadratic-quartic functional equations

In this article, we introduce a class of the generalized mixed additive, quadratic and quartic functional equations and obtain their common solutions. We also investigate the stability of such modified functional equations in the non-Archimedean normed spaces by a fixed point method.

متن کامل

Approximate additive and quadratic mappings in 2-Banach spaces and related topics

Won{Gil Park [Won{Gil Park, J. Math. Anal. Appl., 376 (1) (2011) 193{202] proved the Hyers{Ulam stability of the Cauchy functional equation, the Jensen functional equation and the quadraticfunctional equation in 2{Banach spaces. One can easily see that all results of this paper are incorrect.Hence the control functions in all theorems of this paper are not correct. In this paper, we correctthes...

متن کامل

Non-Archimedean stability of Cauchy-Jensen Type functional equation

In this paper we investigate the generalized Hyers-Ulamstability of the following Cauchy-Jensen type functional equation$$QBig(frac{x+y}{2}+zBig)+QBig(frac{x+z}{2}+yBig)+QBig(frac{z+y}{2}+xBig)=2[Q(x)+Q(y)+Q(z)]$$ in non-Archimedean spaces

متن کامل

Approximate a quadratic mapping in multi-Banach spaces, a fixed point approach

Using the fixed point method, we prove the generalized Hyers-Ulam-Rassias stability of the following functional equation in multi-Banach spaces:begin{equation} sum_{ j = 1}^{n}fBig(-2 x_{j} + sum_{ i = 1, ineq j}^{n} x_{i}Big) =(n-6) fBig(sum_{ i = 1}^{n} x_{i}Big) + 9 sum_{ i = 1}^{n}f(x_{i}).end{equation}

متن کامل

On the stability of set-valued functional equations with the fixed point alternative

* Correspondence: baak@hanyang. ac.kr Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, South Korea Full list of author information is available at the end of the article Abstract Using the fixed point method, we prove the Hyers-Ulam stability of a Cauchy-Jensen type additive set-valued functional equation, a Jensen type additive-quadratic se...

متن کامل

Quadratic $alpha$-functional equations

In this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-Archimedean number with $alpha^{-2}neq 3$. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the quadratic $alpha$-functional equation (0.1) in non-Archimedean Banach spaces.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • J. Applied Mathematics

دوره 2011  شماره 

صفحات  -

تاریخ انتشار 2011