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- Title
Ostrowski-Type Fractional Integral Inequalities: A Survey.
- Authors
Tariq, Muhammad; Ntouyas, Sotiris K.; Ahmad, Bashir
- Abstract
This paper presents an extensive review of some recent results on fractional Ostrowski-type inequalities associated with a variety of convexities and different kinds of fractional integrals. We have taken into account the classical convex functions, quasi-convex functions, (ζ , m) -convex functions, s-convex functions, (s , r) -convex functions, strongly convex functions, harmonically convex functions, h-convex functions, Godunova-Levin-convex functions, M T -convex functions, P-convex functions, m-convex functions, (s , m) -convex functions, exponentially s-convex functions, (β , m) -convex functions, exponential-convex functions, ζ ¯ , β , γ , δ -convex functions, quasi-geometrically convex functions, s − e -convex functions and n-polynomial exponentially s-convex functions. Riemann–Liouville fractional integral, Katugampola fractional integral, k-Riemann–Liouville, Riemann–Liouville fractional integrals with respect to another function, Hadamard fractional integral, fractional integrals with exponential kernel and Atagana-Baleanu fractional integrals are included. Results for Ostrowski-Mercer-type inequalities, Ostrowski-type inequalities for preinvex functions, Ostrowski-type inequalities for Quantum-Calculus and Ostrowski-type inequalities of tensorial type are also presented.
- Subjects
FRACTIONAL integrals; HADAMARD matrices; KERNEL functions; CONVEX functions; RIEMANNIAN metric
- Publication
Foundations (2673-9321), 2023, Vol 3, Issue 4, p660
- ISSN
2673-9321
- Publication type
Article
- DOI
10.3390/foundations3040040