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

Language:: English

Publication timeframe:: 3 times per year
Journal Subjects:: Mathematics, Analysis, Differential Equations and Dynamical Systems, Probability and Statistics, Numerical and Computational Mathematics

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

Artion Kashuri

Rozana Liko

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