In this paper, the authors investigate the generalized Ulam-Hyers stability of a Leibniz type additive and quadratic functional equation ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − − + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − + + − + − + − 3 2 3 3 = ) ( ) ( ) ( z y x f t z y x f t z f t y f t x f ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + − − + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − + − + 3 2 3 2 z y x f z y x f in the setting of intuitionistic fuzzy normed spaces using direct and fixed point methods.

We approximate a fuzzy almost quadratic function by a quadratic function in a fuzzy sense. More precisely, we establish a fuzzy Hyers–Ulam–Rassias stability of the quadratic functional equation f(x + y) + f(x − y) = 2f(x) + 2f(y). Our result can be regarded as a generalization of the stability phenomenon in the framework of normed spaces. We also prove a generalized version of fuzzy stability o...

In this paper, we prove the generalized Hyers-Ulam-Rassias stability for the Drygas functional equation$$f(x+y)+f(x-y)=2f(x)+f(y)+f(-y)$$ in Banach spaces by using the Brzc{d}ek's fixed point theorem. Moreover, we give a general result on the hyperstability of this equation. Our results are improvements and generalizations of the main result of M. Piszczek and J. Szczawi'{n}ska [21].

we investigate the stability of generalizedderivations on banach algebras with a bounded central approximateidentity. we show that every approximate generalized derivation inthe sense of rassias, is an exact generalized derivation. also thestability problem of generalized derivations on the faithful banachalgebras is investigated.

in this paper, we investigate the generalizedhyers--ulam stability of the functional equation

* Correspondence: [email protected]. kr Department of Mathematics, Daejin University, Kyeonggi 487711, Korea Full list of author information is available at the end of the article Abstract Using fixed point method, we investigate the Hyers-Ulam stability and the superstability of partial generalized Jordan derivations on Banach modules related to Jensen type functional equations. Mathematics Subj...

In this paper, we investigate Jordan ∗-homomorphisms on C∗-algebras associated with the following functional inequality ‖f( b−a 3 ) + f( a−3c 3 ) + f( 3a+3c−b 3 )‖ ≤ ‖f(a)‖. We moreover prove the superstability and the generalized Hyers-Ulam stability of Jordan ∗homomorphisms on C∗-algebras associated with the following functional equation f( b− a 3 ) + f( a− 3c 3 ) + f( 3a+ 3c− b 3 ) = f(a).

Abstract In this paper, we unify the system of functional equations defining a multi-quadratic–cubic mapping to single equation. Applying fixed point theorem, study generalized Hyers–Ulam stability mappings. As result, investigate hyperstability mappings in some senses.

‎In 1897‎, ‎Hensel introduced a normed space which does‎ ‎not have the Archimedean property‎. ‎During the last three decades‎ ‎theory of non--Archimedean spaces has gained the interest of‎ ‎physicists for their research in particular in problems coming‎ ‎from quantum physics‎, ‎p--adic strings and superstrings‎. ‎In this paper‎, ‎we prove‎ ‎the generalized Hyers--Ulam--Rassias stability for a‎ ...

in this paper, we obtain the general solution and the generalized  hyers--ulam--rassias stability in random normed spaces, in non-archimedean spacesand also in $p$-banach spaces and finally the stability viafixed point method for a functional equationbegin{align*}&d_f(x_{1},.., x_{m}):= sum^{m}_{k=2}(sum^{k}_{i_{1}=2}sum^{k+1}_{i_{2}=i_{1}+1}... sum^{m}_{i_{m-k+1}=i_{m-k}+1}) f(sum^{m}_{i=1...