Generalized Ostrowski-type inequalities involving second derivatives via the Katugampola fractional integrals

Volume 12, Issue 8, pp 509--522 http://dx.doi.org/10.22436/jnsa.012.08.02

Publication Date: March 18, 2019 Submission Date: December 27, 2018 Revision Date: February 20, 2019 Accteptance Date: February 28, 2019

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Authors

Seth Kermausuor - Department of Mathematics and Computer Science, Alabama State University, Montgomery, AL 36101, USA.

Abstract

In this paper, we provide some Ostrowski-type integral inequalities for functions whose second derivatives belongs to the Lebesgue \(L_q\) spaces using the Katugampola fractional integrals. We also introduced some new inequalities of Ostrowski-type for functions whose second derivatives in absolute value at some powers are strongly \((s, m)\)-convex with modulus \(\mu\geq0\) (in the second sense). Our results are generalizations of some earlier results in the literature.

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Keywords

• Ostrowski inequality
• convex functions
• strongly \((s, m)\)-convex functions
• Riemann--Liouville fractional integrals
• Hadamard fractional integrals
• Katugampola fractional integrals
• Hölder's inequality
• power mean inequality

MSC

•  26A33
•  26A51
•  26D10
•  26D15

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