Artion Kashuri, Rozana Liko, Some new integral inequalities for the generalized $(s,m,\varphi)$-preinvex Godunova-Levin functions of the second kind, Vol. 2017 (2017), Article ID 31, pp. 1-15

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DOI: 10.23952/cot.2017.31

Received July 5, 2017; Accepted October 13, 2017; Published October 20, 2017

Abstract. In this paper, we introduce a new classes of generalized $(s,m,\varphi)$-preinvex Godunova-Levin functions of the second kind. Some characterization theorems and some new integral inequalities for the left-hand side of the Gauss-Jacobi type quadrature formula involving generalized $(s,m,\varphi)$-preinvex Godunova-Levin functions of the second kind along with the beta function are established. Some extensions integral inequalities involving generalized $(h,(m,\varphi))$-preinvex functions are also given.

Artion Kashuri, Rozana Liko, Some new integral inequalities for the generalized $(s,m,\varphi)$-preinvex Godunova-Levin functions of the second kind, Communications in Optimization Theory, Vol. 2017 (2017), Article ID 31, pp. 1-15.