Let be the set of real numbers, , , and . As classical and versions of the Hyers-Ulam stability of the logarithmic type functional equation in a restricted domain, we consider the following inequalities: , and in the sectors . As consequences of the results, we obtain asymptotic behaviors of the previous inequalities. We also consider its distributional version , where , , , , , and the inequality means that for all test functions .
"Stability of a Logarithmic Functional Equation in Distributions on a Restricted Domain." Abstr. Appl. Anal. 2013 (SI58) 1 - 9, 2013. https://doi.org/10.1155/2013/751680