TY - JOUR
AU - Artion Kashuri
AU - Rozana Liko
AU - Silvestru Sever Dragomir
PY - 2018/12/25
Y2 - 2020/02/18
TI - Some new Gauss-Jacobi and Hermite-Hadamard type inequalities concerning $(n+1)$-differentiable generalized $((h_{1},h_{2});(\eta_{1},\eta_{2}))$-convex mappings
JF - Tamkang Journal of Mathematics
JA - Tamkang J. Math.
VL - 49
IS - 4
SE - Papers
DO - 10.5556/j.tkjm.49.2018.2772
UR - https://journals.math.tku.edu.tw/index.php/TKJM/article/view/2772
AB - In this article, we first introduced a new class of generalized $((h_{1},h_{2});(\eta_{1},\eta_{2}))$-convex mappings and two interesting lemmas regarding Gauss-Jacobi and\\ Hermite-Hadamard type integral inequalities. By using the notion of generalized\\ $((h_{1},h_{2});(\eta_{1},\eta_{2}))$-convexity and the first lemma as an auxiliary result, some new estimates with respect to Gauss-Jacobi type integral inequalities are established. Also, using the second lemma, some new estimates with respect to Hermite-Hadamard type integral inequalities via Caputo $k$-fractional derivatives are obtained. It is pointed out that some new special cases can be deduced from main results of the article.
ER -