<abstract xmlns="http://www.w3.org/1999/xhtml"><p> In this paper, the notion of generalized (s; m; ξ)-preinvex function is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving generalized (s; m; ξ)-preinvex functions along with beta function are given. Moreover, we establish some new Hermite-Hadamard type integral inequalities for products of two generalized (s; m; ξ)-preinvex functions via classical and Riemann-Liouville fractional integrals. These results not only extend the results appeared in the literature (see [10],[11]), but also provide new estimates on these types. At the end, some conclusions are given.</p></abstract>

In this paper, the notion of generalized (s; m; ξ)-preinvex function is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving generalized (s; m; ξ)-preinvex functions along with beta function are given. Moreover, we establish some new Hermite-Hadamard type integral inequalities for products of two generalized (s; m; ξ)-preinvex functions via classical and Riemann-Liouville fractional integrals. These results not only extend the results appeared in the literature (see [10],[11]), but also provide new estimates on these types. At the end, some conclusions are given.

Hermite-Hadamard type integral inequalities for products of two generalized (s; m; ξ)-preinvex functions

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

In this paper, the notion of generalized (s; m; ξ)-preinvex function is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi...

Hermite-Hadamard type integral inequalities for products of two generalized (s; m; ξ)-preinvex functions

Published Online: Aug 01, 2017

Page range: 102 - 115

DOI: https://doi.org/10.1515/mjpaa-2017-0009

Keywords
Hermite-Hadamard type inequality, Hölder’s inequality, power mean inequality, Young’s inequality, Riemann-Liouville fractional integral, s-convex in the second sense, m-invex, P-function

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Hermite-Hadamard type integral inequalities for products of two generalized (s; m; ξ)-preinvex functions

Published Online: Aug 01, 2017

Page range: 102 - 115

DOI: https://doi.org/10.1515/mjpaa-2017-0009

KeywordsHermite-Hadamard type inequality, Hölder’s inequality, power mean inequality, Young’s inequality, Riemann-Liouville fractional integral, s-convex in the second sense, m-invex, P-function

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Hermite-Hadamard type inequality, Hölder’s inequality, power mean inequality, Young’s inequality, Riemann-Liouville fractional integral, s-convex in the second sense, m-invex, P-function