Hermite-Jensen-Mercer type inequalities via Ψ-Riemann-Liouville <em>k</em>-fractional integrals

• Main Authors: Saad Ihsan Butt, Artion Kashuri, Muhammad Umar, Adnan Aslam, Wei Gao
• Format: Article
• Language: English
• Published: AIMS Press 2020-07-01
• Series: AIMS Mathematics
• Subjects: convex function; hermite-hadamard inequality; jensen inequality; jensen-mercer inequality; hölder inequality; improved power mean integral inequality; <i>ψ</i>-riemann-liouville <i>k</i>-fractional integrals
• Online Access: https://www.aimspress.com/article/10.3934/math.2020334/fulltext.html

Integral inequalities involving various fractional integral operators are used to solve many fractional differential equations. In this paper, authors prove some Hermite-Jensen-Mercer type inequalities using Ψ-Riemann-Liouville <em>k</em>-Fractional integrals via convex functions. We established some new Ψ-Riemann-Liouville <em>k</em>-Fractional integral inequalities. We also give Ψ-Riemann-Liouville <em>k</em>-Fractional integrals identities for differentiable mapping, and these will be used to derive estimates for some fractional Hermite-Jensen-Mercer type inequalities. Some known results are recaptured from our results as special cases.