Cauchy type functional equations related to some associative rational functions

On Cauchy-type functional equations

LetG be a Hausdorff topological locally compact group. LetM(G) denote the Banach algebra of all complex and bounded measures on G. For all integers n ≥ 1 and all μ ∈ M(G), we consider the functional equations ∫ G f(xty)dμ(t) = ∑n i=1gi(x)hi(y), x,y ∈ G, where the functions f , {gi}, {hi}: G → C to be determined are bounded and continuous functions on G. We show how the solutions of these equati...

Cm Solutions of Some Functional Equations of Associative Type

In this note we give the continuous solutions of some functional equations of associative type that are strictly monotonic in each variable. Neither solvability nor differentiability conditions will be assumed.

Niho Type Cross-Correlation Functions and Related Equations Niho Type Cross-Correlation Functions and Related Equations

Non-Archimedean stability of Cauchy-Jensen Type functional equation

In this paper we investigate the generalized Hyers-Ulamstability of the following Cauchy-Jensen type functional equation$$QBig(frac{x+y}{2}+zBig)+QBig(frac{x+z}{2}+yBig)+QBig(frac{z+y}{2}+xBig)=2[Q(x)+Q(y)+Q(z)]$$ in non-Archimedean spaces

Associative rational functions in two variables⋆

A rational function R(x, y) over a field is said to be associative if R(R(x, y), z) = R(x,R(y, z)). Associative rational functions over a field define group laws on subsets of the field (plus the point at infinity). In this paper, all the associative rational functions of two variables over an arbitrary field are determined and consequently all the groups obtainable from such functions are dete...