The functional equation $f(xy)+f(xy\sp{-1})=2f(x)f(y)$ for groups

The Functional Equation of D’alembert’s Type for Commutative Groups

A functional equation of the form l(x+Y) + 2(x-Y) [. ei(x) 8i(y), 1 where functions i,2,i,8i, i l,...,n are defined on a co:,utatlve group, is solved. We also obtain conditions for the solutions of this equation to be matrix elements of a finite dimensional representation of the group.

stability of the quadratic functional equation

In the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{E}$$ isgiven where $sigma$ is an involution of the normed space $E$ and$k$ is a fixed positive integer. Furthermore we investigate theHyers-Ulam-Rassias stability of the functional equation. TheHyers-Ulam stability on unbounded domains is also studied.Applic...

Application of the Kudryashov method and the functional variable method for the complex KdV equation

In this present work, the Kudryashov method and the functional variable method are used to construct exact solutions of the complex KdV equation. The Kudryashov method and the functional variable method are powerful methods for obtaining exact solutions of nonlinear evolution equations.

On the stability of Jensen’s functional equation on groups

Abstract. In this paper we establish the stability of Jensen’s functional equation on some classes of groups. We prove that Jensen equation is stable on noncommutative groups such as metabelian groups and T (2,K), where K is an arbitrary commutative field with characteristic different from two. We also prove that any group A can be embedded into some group G such that the Jensen functional equa...

On the Stability of the Orthogonally Quartic Functional Equation