Journal
AIMS MATHEMATICS
Volume 5, Issue 5, Pages 5193-5220Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/math.2020334
Keywords
convex function; Hermite-Hadamard inequality; Jensen inequality; Jensen-Mercer inequality; Holder inequality; improved power mean integral inequality; psi-Riemann-Liouville k-Fractional integrals
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Funding
- H.E.C. Pakistan under NRPU project [7906]
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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 Psi-Riemann-Liouville k-Fractional integrals via convex functions. We established some new Psi-Riemann-Liouville k-Fractional integral inequalities. We also give Psi-Riemann-Liouville k-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.
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