On the Stability of Quadratic Functional Equation

ثبت نشده
چکیده

Aoki,T. , (1950) "On stability of the linear transformation in Banach spaces," Journal of the Mathematical Society of Japan, 2,64-66 Chang, S. and Kim,H. M. , (2002), On the Hyer-Ulam stability of a quadratic functional equations, J. Ineq. Appl. Math. , 33, 1-12. Chang,S. , Lee,E. H. and Kim,H. M. , (2003)On the Hyer-Ulam Rassias stability of a quadratic functional equations, Math. Ineq. Appl. Math. , 6(1), 87-95. Cholewa,P. W (1984) Remarks on the stability of functional equations, Aequationes Math. , 27, 76-86. Czerwik,S. , (1992),On the stability of a quadratic mappings in normed spaces, Abh. Math. Sem. Univ. Hamburg. ,62, 59-64. Gavruta,P. , (1994) A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. , 184,431-436.

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

stability of the quadratic functional equation

In the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{E}$$ isgiven where $sigma$ is an involution of the normed space $E$ and$k$ is a fixed positive integer. Furthermore we investigate theHyers-Ulam-Rassias stability of the functional equation. TheHyers-Ulam stability on unbounded domains is also studied.Applic...

متن کامل

2-Banach stability results for the radical cubic functional equation related to quadratic mapping

The aim of this paper is to introduce and solve the generalized radical cubic functional equation related to quadratic functional equation$$fleft(sqrt[3]{ax^{3}+by^{3}}right)+fleft(sqrt[3]{ax^{3}-by^{3}}right)=2a^{2}f(x)+2b^{2}f(y),;; x,yinmathbb{R},$$for a mapping $f$ from $mathbb{R}$ into a vector space. We also investigate some stability and hyperstability results for...

متن کامل

Intuitionistic fuzzy stability of a quadratic and quartic functional equation

In this paper, we prove the generalized Hyers--Ulamstability of a quadratic and quartic functional equation inintuitionistic fuzzy Banach spaces.

متن کامل

Stability of the quadratic functional equation in non-Archimedean L-fuzzy normed spaces

In this paper, we prove the generalized Hyers-Ulam stability of the quadratic functionalequation$$f(x+y)+f(x-y)=2f(x)+2f(y)$$in non-Archimedean $mathcal{L}$-fuzzy normed spaces.

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

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

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:

دوره   شماره 

صفحات  -

تاریخ انتشار 2018