Some New Integral Inequalities for <i>n</i>-times Differentiable <i>s</i>- Convex functions in the first sense

Abstract

In this work, by using an integral identity together with both the Hölder and the Power-Mean integral inequality we establish several new inequalities for n-time differentiable -convex functions in the first sense.

Some new integral inequalities for N-times differentiable R-convex and R-concave functions

“…Convexity theory has appeared as a powerful technique to study a wide class of unrelated problems in pure and applied sciences. Many articles have been written by a number of mathematicians on convex functions and inequalities for their different classes, using, for example, the last articles [3,[8][9][10][11][12][13][14][15] and the references in these papers.…”

Some new integral inequalities for functions whose nth derivatives in absolute value are (?, m)-convex functions

“…(i) In case of m = 1 and α = s, the results are obtained in this paper reduce to the results obtained for s-convex functions in the first sense in [14]. (ii) In case of α = m = 1, the results are obtained in this paper reduce to the results obtained for convex functions in [16].…”

Geometric trigonometrically convexity and better approximations

“…It is well known that convexity theory provides strong principles and methods to study a wide range of problems in both mathematics and many other sciences. See articles [1–5] and the references therein.…”