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<p/> <p>Let <inline-formula><graphic file="1687-1847-2010-432796-i1.gif"/></inline-formula> be the set of positive real numbers, <inline-formula><graphic file="1687-1847-2010-432796-i2.gif"/></inline-formula> a Banach space, <inline-formula><graphic file="1687-1847-2010-432796-i3.gif"/></inline-formula> and <inline-formula><graphic file="1687-1847-2010-432796-i4.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2010-432796-i5.gif"/></inline-formula> with <inline-formula><graphic file="1687-1847-2010-432796-i6.gif"/></inline-formula>. We prove the Hyers-Ulam stability of the Jensen type logarithmic functional inequality <inline-formula><graphic file="1687-1847-2010-432796-i7.gif"/></inline-formula> in restricted domains of the form <inline-formula><graphic file="1687-1847-2010-432796-i8.gif"/></inline-formula> for fixed <inline-formula><graphic file="1687-1847-2010-432796-i9.gif"/></inline-formula> with <inline-formula><graphic file="1687-1847-2010-432796-i10.gif"/></inline-formula> or <inline-formula><graphic file="1687-1847-2010-432796-i11.gif"/></inline-formula> and <inline-formula><graphic file="1687-1847-2010-432796-i12.gif"/></inline-formula>. As consequences of the results we obtain asymptotic behaviors of the inequality as <inline-formula><graphic file="1687-1847-2010-432796-i13.gif"/></inline-formula>.</p>