Convex solutions of a functional equation arising in information theory Export

@article{citeulike:3196695, abstract = {Given a convex function f defined for positive real variables, the so-called Csisz\'{a}r f-divergence is a function If defined for two n-dimensional probability vectors p=(p1,...,pn) and q=(q1,...,qn) as . For this generalized measure of entropy to have distance-like properties, especially symmetry, it is necessary for f to satisfy the following functional equation: for all x>0. In the present paper we determine all the convex solutions of this functional equation by proposing a way of generating all of them. In doing so, existing usual f-divergences are recovered and new ones are proposed.}, author = {Hiriart-Urruty, J. B. and Mart\'{\i}nez-Legaz, J. E.}, citeulike-article-id = {3196695}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/j.jmaa.2006.06.035}, citeulike-linkout-1 = {http://www.sciencedirect.com/science/article/B6WK2-4KDBMCD-7/2/93c55b63c968a17e49096a174f880797}, day = {15}, doi = {10.1016/j.jmaa.2006.06.035}, journal = {Journal of Mathematical Analysis and Applications}, keywords = {convexity, f-divergence, information, theory}, month = {April}, number = {2}, pages = {1309--1320}, posted-at = {2008-09-05 06:00:59}, priority = {4}, title = {Convex solutions of a functional equation arising in information theory}, url = {http://dx.doi.org/10.1016/j.jmaa.2006.06.035}, volume = {328}, year = {2007} }

TY - JOUR ID - citeulike:3196695 L3 - citeulike-article-id:3196695 N2 - Given a convex function f defined for positive real variables, the so-called Csiszár f-divergence is a function If defined for two n-dimensional probability vectors p=(p1,...,pn) and q=(q1,...,qn) as . For this generalized measure of entropy to have distance-like properties, especially symmetry, it is necessary for f to satisfy the following functional equation: for all x>0. In the present paper we determine all the convex solutions of this functional equation by proposing a way of generating all of them. In doing so, existing usual f-divergences are recovered and new ones are proposed. IS - 2 JF - Journal of Mathematical Analysis and Applications EP - 1320 TI - Convex solutions of a functional equation arising in information theory VL - 328 SP - 1309 KW - convexity KW - f-divergence KW - information KW - theory AU - Hiriart-Urruty, JB AU - Martínez-Legaz, JE PY - 2007/04/15/ UR - http://dx.doi.org/10.1016/j.jmaa.2006.06.035 ER -