Some Inequalities for Differentiable Mappings and Applications to Fejér Inequality and Weighted Trapezoidal Formula

On The Hermite- Hadamard-Fejér Type Integral Inequality for Convex Function

“…The most well-known inequalities related to the integral mean of a convex function are the Hermite Hadamard inequalities or its weighted versions, the so-called HermiteHadamardFejér inequalities (see, [8,13,14,15,16,19,20]). In [7], Fejer gave a weighted generalizatinon of the inequalities (1.1) as the following: …”

New Hermite Hadamard type inequalities for twice differentiable convex mappings via Green function and applications

“…If we substitute (10) and (12) in (9), then we easily deduce required inequality (8) which completes the proof. Now, we establish trapezoid inequality in a different way by using convexity of |f | q .…”

“…Hermite Hadamard's inequality (1), for example, is significant in its rich geometry and hence there are many studies on it to demonstrate its new proofs, refinements, extensions and generalizations. You can check ( [1], [2], [4], [5] and [10]- [15]) and the references included there.…”

Some Hermite-Hadamard-Fejér Type Integral Inequalities for Differentiable η-Convex Functions with Applications

“…For various types of (1) and more results related to generalized Hermite-Hadamard-Fejér inequality, see [2][3][4][5][6][7][8] and references therein. On the other hand, the concept of -convex functions, firstly named by -convex functions, as generalization of convex functions has been introduced in [9].…”