Some logarithmic functional equations
Vichian Laohakosol; Watcharapon Pimsert; Charinthip Hengkrawit; Bruce Ebanks
Archivum Mathematicum (2012)
- Volume: 048, Issue: 3, page 173-181
- ISSN: 0044-8753
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topLaohakosol, Vichian, et al. "Some logarithmic functional equations." Archivum Mathematicum 048.3 (2012): 173-181. <http://eudml.org/doc/247004>.
@article{Laohakosol2012,
abstract = {The functional equation $f(y-x) - g(xy) = h\left(1/x-1/y\right)$ is solved for general solution. The result is then applied to show that the three functional equations $f(xy)=f(x)+f(y)$, $f(y-x)-f(xy)=f(1/x-1/y)$ and $f(y-x)-f(x)-f(y)=f(1/x-1/y)$ are equivalent. Finally, twice differentiable solution functions of the functional equation $f(y-x) - g_1(x)-g_2(y) = h\left(1/x-1/y\right)$ are determined.},
author = {Laohakosol, Vichian, Pimsert, Watcharapon, Hengkrawit, Charinthip, Ebanks, Bruce},
journal = {Archivum Mathematicum},
keywords = {logarithmic functional equation; Pexider equations; logarithmic functional equation; Pexider-type functional equation},
language = {eng},
number = {3},
pages = {173-181},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Some logarithmic functional equations},
url = {http://eudml.org/doc/247004},
volume = {048},
year = {2012},
}
TY - JOUR
AU - Laohakosol, Vichian
AU - Pimsert, Watcharapon
AU - Hengkrawit, Charinthip
AU - Ebanks, Bruce
TI - Some logarithmic functional equations
JO - Archivum Mathematicum
PY - 2012
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 048
IS - 3
SP - 173
EP - 181
AB - The functional equation $f(y-x) - g(xy) = h\left(1/x-1/y\right)$ is solved for general solution. The result is then applied to show that the three functional equations $f(xy)=f(x)+f(y)$, $f(y-x)-f(xy)=f(1/x-1/y)$ and $f(y-x)-f(x)-f(y)=f(1/x-1/y)$ are equivalent. Finally, twice differentiable solution functions of the functional equation $f(y-x) - g_1(x)-g_2(y) = h\left(1/x-1/y\right)$ are determined.
LA - eng
KW - logarithmic functional equation; Pexider equations; logarithmic functional equation; Pexider-type functional equation
UR - http://eudml.org/doc/247004
ER -
References
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