Ostrowski type inequalities for functions whose derivatives are strongly (a,m)-convex via k-Riemann-Liouville fractional integrals

Abstract

In this paper, we provide some Ostrowski type integral inequalities for functions whose derivatives in absolute value at some powers are strongly (α, m)convex with modulus µ ≥ 0 via the k-Riemann-Liouville fractional integrals. Similar results related to (α, m)-convex functions are obtained as a particular case.

Simpson’s type inequalities for η-convex functions via k-Riemann–Liouville fractional integrals

“…For more information and some results related to this integral operator, we refer the interested reader to [8,[11][12][13] and the references therein.…”

On the Generalization of Ostrowski-Type Integral Inequalities via Fractional Integral Operators with Application to Error Bounds

“…For instance, using s-convex and h-convex functions, Set [3] and Liu [4] demonstrated the Ostrowski-type inequality for Riemann-Liouville fractional integrals. The Ostrowski-type inequalities for Riemann-Liouville k-fractional integrals were provided by Kermausuor [5] and Lakhal [6] via strongly (a, m)-convex functions and k − beta-convex functions.…”

Inequalities of the Ostrowski Type Associated with Fractional Integral Operators Containing the Mittag–Leffler Function

“…For example, Set [4] and Liu [5] proved the Ostrowski-type inequalities for Riemann-Liouville fractional integrals via s-convex and h-convex functions. Kermausuor [6] and Lakhal [7] gave the Ostrowski-type inequalities for Riemann-Liouville k-fractional integrals via strongly (α, m)convex functions and k − β-convex functions. In [8], Set et al proved the Ostrowski-type inequalities for conformable fractional integrals via convex and AG-convex functions.…”