Some logarithmic functional equations

Abstract

The functional equation /(y -x) -g{xy) = h (l/i -1/y) is solved for general solution. The result is then applied to show that the three functional equations f{xy) = f(x) + f{y), f{y-x)-f{xy) = /(1/x-l/y) and f{y-x)-f{x) -f(y) = f{l/x -l/y) are equivalent. Finally, twice differentiable solution functions of the functional equation f{y -i) -gi{x) -g2(y) = h {l/x -\/y) are determined. 2010 Mathematics Subject Classification: primary 39B20.

Pexiderization of some logarithmic functional equations

“…where a ∈ R is a constant. Finally, we get from (6), (10) and 9that The converse can be easily obtained by a simple calculation.…”

“…In [10], the authors complemented the works [4], [8] and [9] mentioned above by solving a few other logarithmic functional equations in Pexider form.…”