On Hyers-ulam Stability of Generalized Wilson’s Equation
نویسندگان
چکیده
In this paper, we study the Hyers-Ulam stability problem for the following functional equation (E(K)) ∑ φ∈Φ ∫ K f(xkφ(y)k)dωK(k) = |Φ|f(x)g(y), x, y ∈ G, where G is a locally compact group, K is a compact subgroup of G, ωK is the normalized Haar measure of K, Φ is a finite group of K-invariant morphisms of G and f, g : G −→ C are continuous complex-valued functions such that f satisfies the Kannappan type condition, for all x, y, z ∈ G (*) ∫ K ∫ K f(zkxkhyh)dωK(k)dωK(h) = ∫ K ∫ K f(zkykhxh)dωK(k)dωK(h). Our results generalize and extend the Hyers-Ulam stability obtained for the Wilson’s functional equation.
منابع مشابه
Hyers-Ulam-Rassias stability of a composite functional equation in various normed spaces
In this paper, we prove the generalized Hyers-Ulam(or Hyers-Ulam-Rassias ) stability of the following composite functional equation f(f(x)-f(y))=f(x+y)+f(x-y)-f(x)-f(y) in various normed spaces.
متن کاملA new method for the generalized Hyers-Ulam-Rassias stability
We propose a new method, called the textit{the weighted space method}, for the study of the generalized Hyers-Ulam-Rassias stability. We use this method for a nonlinear functional equation, for Volterra and Fredholm integral operators.
متن کاملApproximate solutions of homomorphisms and derivations of the generalized Cauchy-Jensen functional equation in $C^*$-ternary algebras
In this paper, we prove Hyers-Ulam-Rassias stability of $C^*$-ternary algebra homomorphism for the following generalized Cauchy-Jensen equation $$eta mu fleft(frac{x+y}{eta}+zright) = f(mu x) + f(mu y) +eta f(mu z)$$ for all $mu in mathbb{S}:= { lambda in mathbb{C} : |lambda | =1}$ and for any fixed positive integer $eta geq 2$ on $C^*$-ternary algebras by using fixed poind alternat...
متن کاملThe Generalized Hyers-ulam-rassias Stability of a Quadratic Functional Equation
In this paper, we investigate the generalized Hyers Ulam Rassias stability of a new quadratic functional equation f(2x + y) + f(2x− y) = 2f(x + y) + 2f(x− y) + 4f(x)− 2f(y). Generalized Hyers-Ulam-Rassias Stability K. Ravi, R. Murali and M. Arunkumar vol. 9, iss. 1, art. 20, 2008 Title Page
متن کاملA new type of Hyers-Ulam-Rassias stability for Drygas functional equation
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].
متن کامل