<abstract xmlns="http://www.w3.org/1999/xhtml"><p>A generalization of the Hermite–Hadamard (HH) inequality for a positive convex stochastic process, by means of a newly proposed fractional integral operator, is hereby established. Results involving the Riemann– Liouville, Hadamard, Erdélyi–Kober, Katugampola, Weyl and Liouville fractional integrals are deduced as particular cases of our main result. In addition, we also apply some known HH results to obtain some estimates for the expectations of integrals of convex and <italic>p</italic>-convex stochastic processes. As a side note, we also pointed out a mistake in the main result of the paper [<italic>Hermite–Hadamard type inequalities, convex stochastic processes and Katugampola fractional integral</italic>, Revista Integración, temas de matemáticas <bold>36</bold> (2018), no. 2, 133–149]. We anticipate that the idea employed herein will inspire further research in this direction.</p></abstract>

A generalization of the Hermite–Hadamard (HH) inequality for a positive convex stochastic process, by means of a newly proposed fractional integral operator, is hereby established. Results involving the Riemann– Liouville, Hadamard, Erdélyi–Kober, Katugampola, Weyl and Liouville fractional integrals are deduced as particular cases of our main result. In addition, we also apply some known HH results to obtain some estimates for the expectations of integrals of convex and p-convex stochastic processes. As a side note, we also pointed out a mistake in the main result of the paper [Hermite–Hadamard type inequalities, convex stochastic processes and Katugampola fractional integral, Revista Integración, temas de matemáticas 36 (2018), no. 2, 133–149]. We anticipate that the idea employed herein will inspire further research in this direction.

Generalized Fractional Inequalities of the Hermite–Hadamard Type for Convex Stochastic Processes

Department of Mathematics and Computer Science

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution 4.0 International License.

A generalization of the Hermite–Hadamard (HH) inequality for a positive convex stochastic process, by means of a newly proposed fractional integral operator,...

Generalized Fractional Inequalities of the Hermite–Hadamard Type for Convex Stochastic Processes

Published Online: Dec 17, 2020

Page range: 90 - 104

Received: Feb 09, 2020

Accepted: Nov 24, 2020

DOI: https://doi.org/10.2478/amsil-2020-0026

Keywords
Hermite–Hadamard inequalities, generalized Katugampola fractional integrals, generalized Riemann–Liouville fractional integral, convex and positive stochastic processes

© 2020 McSylvester Ejighikeme Omaba et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Generalized Fractional Inequalities of the Hermite–Hadamard Type for Convex Stochastic Processes

Published Online: Dec 17, 2020

Page range: 90 - 104

Received: Feb 09, 2020

Accepted: Nov 24, 2020

DOI: https://doi.org/10.2478/amsil-2020-0026

KeywordsHermite–Hadamard inequalities, generalized Katugampola fractional integrals, generalized Riemann–Liouville fractional integral, convex and positive stochastic processes

© 2020 McSylvester Ejighikeme Omaba et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Hermite–Hadamard inequalities, generalized Katugampola fractional integrals, generalized Riemann–Liouville fractional integral, convex and positive stochastic processes