Generalized fractional inequalities of the Hermite-Hadamard type for convex stochastic processes

McSylvester Ejighikeme Omaba; Eze R. Nwaeze

Published: 2020-12-17

Vol. 35 No. 1 (2021)

Generalized fractional inequalities of the Hermite-Hadamard type for convex stochastic processes

McSylvester Ejighikeme Omaba , Eze R. Nwaeze

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.

Keywords:

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

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Omaba, M. E., & Nwaeze, E. R. (2020). Generalized fractional inequalities of the Hermite-Hadamard type for convex stochastic processes. Annales Mathematicae Silesianae, 35(1), 90–104. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13476

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McSylvester Ejighikeme Omaba

Affiliation:

Department of Mathematics College of Science University of Hafr Al Batin, KSA Saudi Arabia

Eze R. Nwaeze

enwaeze@alasu.edu
https://orcid.org/0000-0002-1375-1474

Affiliation:

Department of Mathematics and Computer Science, Alabama State University, USA United States

Vol. 35 No. 1 (2021)
Published: 2021-02-10

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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