Rocky Mountain Journal of Mathematics

Jensen type inequalities and their applications via fractional integrals

Sadegh Abbaszadeh, Ali Ebadian, and Mohsen Jaddi

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Abstract

The present paper is devoted to the study of Jensen type inequalities for fractional integration on finite subintervals of the real axis. The complete form of Jensen's inequality and the generalized Jensen's inequality are investigated by using the Chebyshev inequality. As applications, some new integral inequalities, including Holder's and Minkowski's inequalities, are obtained by using Jensen's inequality via Riemann-Liouville fractional integrals.

Article information

Source
Rocky Mountain J. Math., Volume 48, Number 8 (2018), 2459-2488.

Dates
First available in Project Euclid: 30 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1546138817

Digital Object Identifier
doi:10.1216/RMJ-2018-48-8-2459

Mathematical Reviews number (MathSciNet)
MR3894989

Zentralblatt MATH identifier
06999270

Subjects
Primary: 26A33: Fractional derivatives and integrals 26D15: Inequalities for sums, series and integrals 28A25: Integration with respect to measures and other set functions

Keywords
Riemann-Liouville fractional integrals Jensen's inequality Holder's inequality Minkowski's inequality

Citation

Abbaszadeh, Sadegh; Ebadian, Ali; Jaddi, Mohsen. Jensen type inequalities and their applications via fractional integrals. Rocky Mountain J. Math. 48 (2018), no. 8, 2459--2488. doi:10.1216/RMJ-2018-48-8-2459. https://projecteuclid.org/euclid.rmjm/1546138817


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