“…Authors of recent decades have studied the inequality (1.2), known as Hermite-Hadamard inequality (or trapezium inequality) in the premises of newly invented definitions due to motivation of convex function. Interested readers can see the references [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,29,30,31]. The stability theory for functional inequalities has its origin in the paper of Hyers and Ulam [13], in which the notion of δ-convex functions is introduced.…”