AbstractThe present work aims to determine the solution f:R2→R of the equation f(ux−vy,uy−vx)=f(x,y)+f(u,v)+f(x,y)f(u,v) for all x,y,u,v∈R without any regularity assumption. The solution of the functional equation f(ux+vy,uy−vx)=f(x,y)+f(u,v)+f(x,y)f(u,v) is also determined. The methods of solution of these equations are simple and elementary. These two equations arise in connection with the characterizations of determinant and permanent of two-by-two symmetric matrices, respectively
8. f (x) + g(y) = h(x + y). Pexider’s equation. Here, the functions f (x), g(y), and h(z) are unkno...
y 1 – x = f (y) + (1 – y)f x 1 – y Basic equation of information theory. Here, x, y, x + y can assum...
By applying the fixed point method, we will prove the Hyers-Ulam-Rassias stability of the functional...
This poster will discuss the solutions of two functional equations that arise in connection with the...
AbstractThe present work aims to determine the solution f:R2→R of the equation f(ux−vy,uy−vx)=f(x,y)...
In this paper, we determine the general solutions of the functional equation f(ux + (L − 1)vy, xv + ...
The main purpose of this paper is to investigate the stability of the functional equation f(x+y,y+z)...
The aim of this paper is to obtain the general solution of a reciprocal functional equation of the f...
. We consider the functional equation f(xy) + f(x + y) = f(xy + x) + f(y) and its pexiderized versio...
AbstractIn this paper, we obtain the general solution and the stability of the 2-variable quadratic ...
Abstract. In this note we give the general solution of the functional equation f (x) f (x+ y) = f (...
In this note, for any given real numbers a, b, c, we determine all the solutions f: R − → R of the f...
This is an expository paper containing remarks on solutions to some functional equations of a form, ...
AbstractIn this paper we study the Hyers–Ulam stability and the superstability of the functional equ...
x, y4(x) = C1 − x1 + C2x, where C, C1, and C2 are arbitrary constants. 2◦. Particular solutions of ...
8. f (x) + g(y) = h(x + y). Pexider’s equation. Here, the functions f (x), g(y), and h(z) are unkno...
y 1 – x = f (y) + (1 – y)f x 1 – y Basic equation of information theory. Here, x, y, x + y can assum...
By applying the fixed point method, we will prove the Hyers-Ulam-Rassias stability of the functional...
This poster will discuss the solutions of two functional equations that arise in connection with the...
AbstractThe present work aims to determine the solution f:R2→R of the equation f(ux−vy,uy−vx)=f(x,y)...
In this paper, we determine the general solutions of the functional equation f(ux + (L − 1)vy, xv + ...
The main purpose of this paper is to investigate the stability of the functional equation f(x+y,y+z)...
The aim of this paper is to obtain the general solution of a reciprocal functional equation of the f...
. We consider the functional equation f(xy) + f(x + y) = f(xy + x) + f(y) and its pexiderized versio...
AbstractIn this paper, we obtain the general solution and the stability of the 2-variable quadratic ...
Abstract. In this note we give the general solution of the functional equation f (x) f (x+ y) = f (...
In this note, for any given real numbers a, b, c, we determine all the solutions f: R − → R of the f...
This is an expository paper containing remarks on solutions to some functional equations of a form, ...
AbstractIn this paper we study the Hyers–Ulam stability and the superstability of the functional equ...
x, y4(x) = C1 − x1 + C2x, where C, C1, and C2 are arbitrary constants. 2◦. Particular solutions of ...
8. f (x) + g(y) = h(x + y). Pexider’s equation. Here, the functions f (x), g(y), and h(z) are unkno...
y 1 – x = f (y) + (1 – y)f x 1 – y Basic equation of information theory. Here, x, y, x + y can assum...
By applying the fixed point method, we will prove the Hyers-Ulam-Rassias stability of the functional...
DOI
Add to ORKG