Some new Gauss-Jacobi and Hermite-Hadamard type inequalities concerning $(n+1)$-differentiable generalized $((h_{1},h_{2});(\eta_{1},\eta_{2}))$-convex mappings
2018 ◽
Vol 49
(4)
◽
pp. 317-337
◽
Keyword(s):
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.
Keyword(s):
Keyword(s):
2020 ◽
Vol 10
(2)
◽
pp. 226-236
Keyword(s):
Keyword(s):
2019 ◽
Vol 26
(1/2)
◽
pp. 41-55
◽
Keyword(s):