TY - JOUR AU - Kashuri, Artion AU - Liko, Rozana AU - Dragomir, Silvestru Sever PY - 2018/12/25 Y2 - 2024/03/28 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 SP - 317-337 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 -