#### Artion Kashuri, Rozana Liko, Some k-fractional integral inequalities of Hermite-Hadamard type concerning twice differentiable generalized relative semi-(r; m, h_1, h_2)-preinvex mappings, Vol. 2018 (2018), Article ID 6, pp. 1-16

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DOI: 10.23952/cot.2018.6

Received October 1, 2017; Accepted February 19, 2018; Published March 8, 2018

Abstract. In this article, we first present some integral inequalities for Gauss-Jacobi type quadrature formula involving generalized relative semi-$(r; m, h_{1}, h_{2})$-preinvex mappings. A new identity concerning twice differentiable mappings defined on m-invex set is derived. Based on the notion of generalized relative semi-$(r; m, h_{1}, h_{2})$-preinvexity and an auxiliary result, some new estimates with respect to Hermite-Hadamard type inequalities via k-fractional integrals are established. It is pointed out that some new special cases can be deduced from the main results of this article.

Artion Kashuri, Rozana Liko, Some k-fractional integral inequalities of Hermite-Hadamard type concerning twice differentiable generalized relative semi-$(r; m, h_1, h_2)$-preinvex mappings, Communications in Optimization Theory, Vol. 2018 (2018), Article ID 6, pp. 1-16.