On stability of functional equations related to quadratic mappings in fuzzy Banach spaces
نویسندگان
چکیده
*Correspondence: [email protected]; [email protected] 2Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia 3Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju, 660-701, Korea Full list of author information is available at the end of the article Abstract In this paper, we establish the generalized Hyers-Ulam stability problem of radical quadratic functional equations f ( √ x2 + y2) = f (x) + f (y) in fuzzy Banach spaces via the direct and fixed point methods. MSC: 39B72; 39B82; 39B52; 47H09
منابع مشابه
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 کاملAsymptotic aspect of quadratic functional equations and super stability of higher derivations in multi-fuzzy normed spaces
In this paper, we introduce the notion of multi-fuzzy normed spaces and establish an asymptotic behavior of the quadratic functional equations in the setup of such spaces. We then investigate the superstability of strongly higher derivations in the framework of multi-fuzzy Banach algebras
متن کاملA Hyers-Ulam-Rassias stability result for functional equations in Intuitionistic Fuzzy Banach spaces
Hyers-Ulam-Rassias stability have been studied in the contexts of several areas of mathematics. The concept of fuzziness and its extensions have been introduced to almost all branches of mathematics in recent times.Here we define the cubic functional equation in 2-variables and establish that Hyers-Ulam-Rassias stability holds for such equations in intuitionistic fuzzy Banach spaces.
متن کامل2-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 کاملIntuitionistic 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