<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In the present paper, the notion of new generalized (<italic>s, m, ϕ</italic>)-preinvex mapping is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving new generalized (<italic>s, m, ϕ</italic>)-preinvex mappings along with beta function are given. Moreover, some generalizations of Ostrowski type inequalities for new generalized (<italic>s, m, ϕ</italic>)-preinvex mappings via conformable fractional integrals are established. At the end, some applications to special means are given.</p></abstract>

In the present paper, the notion of new generalized (s, m, ϕ)-preinvex mapping is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving new generalized (s, m, ϕ)-preinvex mappings along with beta function are given. Moreover, some generalizations of Ostrowski type inequalities for new generalized (s, m, ϕ)-preinvex mappings via conformable fractional integrals are established. At the end, some applications to special means are given.

New conformable fractional integrals of Ostrowski type using new generalized (<italic>s, m, ϕ</italic>)-preinvex mappings

Department of Mathematics, Faculty of Technical Science

Moroccan Journal of Pure and Applied Analysis

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

New conformable fractional integrals of Ostrowski type using new generalized ()-preinvex mappings

In the present paper, the notion of new generalized (s, m, ϕ)-preinvex mapping is introduced and some new integral inequalities for the left-hand side of...

New conformable fractional integrals of Ostrowski type using new generalized (s, m, ϕ)-preinvex mappings

Published Online: Jul 28, 2018

Page range: 173 - 185

Received: Jun 06, 2017

Accepted: May 22, 2018

DOI: https://doi.org/10.1515/mjpaa-2017-0014

Keywords
Ostrowski type inequality, Hölder’s inequality, Power mean inequality, Riemann- Liouville fractional integrals, Conformable fractional integrals, -convex function in the second sense, -invex, -function

© 2018 Artion Kashuri et al., published by Sciendo

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

New conformable fractional integrals of Ostrowski type using new generalized (s, m, ϕ)-preinvex mappings

Published Online: Jul 28, 2018

Page range: 173 - 185

Received: Jun 06, 2017

Accepted: May 22, 2018

DOI: https://doi.org/10.1515/mjpaa-2017-0014

KeywordsOstrowski type inequality, Hölder’s inequality, Power mean inequality, Riemann- Liouville fractional integrals, Conformable fractional integrals, -convex function in the second sense, -invex, -function

© 2018 Artion Kashuri et al., published by Sciendo

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

Keywords
Ostrowski type inequality, Hölder’s inequality, Power mean inequality, Riemann- Liouville fractional integrals, Conformable fractional integrals, -convex function in the second sense, -invex, -function