39B62,26D15.

In the article, a functional inequality in abstract spaces is established, which gives a new affirmative answer to an open problem posed by Feng Qi in [9]. Moreover, some integral inequalities and a discrete inequality involving sums are deduced.

[9] FENG QI, Several integral inequalities, J. Inequal. Pure Appl. Math., 1(2) (2000), Art.19.