Add to ORKG[[abstract]]Let G be an abelian group, C be the field of complex numbers, and 0 6≠α∈ G be a fixed element. In this paper, we determine the general solution f, g : G→C of the functional equation f(x-y+α)+g(x+y+α) = 2 f(x) f(y) for all x; y ∈
In this paper we discuss the composite functional equation f(x+2f(y))=f(x)+y+f(y) on an Abelian gr...
Abstract. We solve the functional equation N−1∑ n=0 g(x+ kn · y) = Ng(x)f(y), x, y ∈ G, where G is ...
AbstractLet f:S→X map an abelian semigroup (S,+) into a Banach space (X‖⋅‖). We deal with stability ...
AbstractThe functional equation f(xy)=f(x)g(y)+g(x)f(y)+h(x)h(y) is solved where f, g, h are complex...
Let (G, +) be a uniquely 2-divisible Abelian group. In the present paper we will consider the soluti...
Abstract. In this note we give the general solution of the functional equation f (x) f (x+ y) = f (...
AbstractThe stability of the functional equation F(x+y)−G(x−y)=2H(x)K(y) over the domain of an abeli...
Abstract. Consider the functional equation f, g, h, k: G → K, f(xy) + g(xy−1) = h(x)k(y) (∗) where ...
The aim of this paper is to investigate the stability problem for the pexiderized trigonometric func...
ABSTRACT. A functional equation of the form l(x+Y) + 2(x-Y) [. ei(x) 8i(y),1 where functions i,2,i,8...
For an abelian group (G,+,0) we consider the functional equation 1 $$f : G \to G, \,\, x + f(y + f(x...
In this paper, we determine the general solutions of the functional equation f(ux + (L − 1)vy, xv + ...
We investigate Pexider--type functional equation $$\max\{f(x+y),f(x-y)\}=f(x)g(y)+h(y),\quad x,y\in ...
In this paper the stability of quadratic functional equation, f(xy)+f(xy-1)=2f(x)+2f(y) on class of ...
. We consider the functional equation f(xy) + f(x + y) = f(xy + x) + f(y) and its pexiderized versio...
In this paper we discuss the composite functional equation f(x+2f(y))=f(x)+y+f(y) on an Abelian gr...
Abstract. We solve the functional equation N−1∑ n=0 g(x+ kn · y) = Ng(x)f(y), x, y ∈ G, where G is ...
AbstractLet f:S→X map an abelian semigroup (S,+) into a Banach space (X‖⋅‖). We deal with stability ...
AbstractThe functional equation f(xy)=f(x)g(y)+g(x)f(y)+h(x)h(y) is solved where f, g, h are complex...
Let (G, +) be a uniquely 2-divisible Abelian group. In the present paper we will consider the soluti...
Abstract. In this note we give the general solution of the functional equation f (x) f (x+ y) = f (...
AbstractThe stability of the functional equation F(x+y)−G(x−y)=2H(x)K(y) over the domain of an abeli...
Abstract. Consider the functional equation f, g, h, k: G → K, f(xy) + g(xy−1) = h(x)k(y) (∗) where ...
The aim of this paper is to investigate the stability problem for the pexiderized trigonometric func...
ABSTRACT. A functional equation of the form l(x+Y) + 2(x-Y) [. ei(x) 8i(y),1 where functions i,2,i,8...
For an abelian group (G,+,0) we consider the functional equation 1 $$f : G \to G, \,\, x + f(y + f(x...
In this paper, we determine the general solutions of the functional equation f(ux + (L − 1)vy, xv + ...
We investigate Pexider--type functional equation $$\max\{f(x+y),f(x-y)\}=f(x)g(y)+h(y),\quad x,y\in ...
In this paper the stability of quadratic functional equation, f(xy)+f(xy-1)=2f(x)+2f(y) on class of ...
. We consider the functional equation f(xy) + f(x + y) = f(xy + x) + f(y) and its pexiderized versio...
In this paper we discuss the composite functional equation f(x+2f(y))=f(x)+y+f(y) on an Abelian gr...
Abstract. We solve the functional equation N−1∑ n=0 g(x+ kn · y) = Ng(x)f(y), x, y ∈ G, where G is ...
AbstractLet f:S→X map an abelian semigroup (S,+) into a Banach space (X‖⋅‖). We deal with stability ...