On Ostrowski type inequalities

By Ravi P. Agarwal, M. Luo, Ravinder Krishna Raina. 2016

55 citations recorded by the source corpus.

Abstract In this paper, new forms of Ostrowski type inequalities are established for a general class of fractional integral operators. The main results are used to derive Ostrowski type inequalities involving the familiar Riemann-Liouville fractional integral operators and other important integral operators. We further obtain similar types of inequalities for the integral operators whose kernels are the Fox-Wright generalized hypergeometric function. Several consequences and special cases of some of the results including applications to Stolarsky’s means are also pointed out.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/40b00b58a03db09fc3494fa27822b653fd6e3538

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In Applied Mathematics

In Statistics and Probability

Citations in the corpus

New General Variants of Chebyshev Type Inequalities via Generalized Fractional Integral Operators (2021, background): “By setting κ = 1 and Φ(t) = t in Definition 3, it is obvious to see that the definition can be reduced to the generalized fractional integral operators that is established by Agarwal (see [26]) and Rania et al.”
On parameterized inequalities of Ostrowski and Simpson type for convex functions via generalized fractional integrals (2021, methodology): “By applying the power mean inequality to the inequality (7), it follows |||Λ1(τ, 1) [(1 − λ)F (τ) + λF(ρ2)] + Δ1(τ, 1) [(1 − μ)F (τ) + μF(ρ1)] − [τ+IφF (ρ2) +τ−IφF (ρ1)]||| ≤ (ρ2 − τ) ⎜⎜⎝ 1 ∫ 0 |λΛ1(τ, 1) − Λ1(τ, ξ)| dξ⎟⎟⎠ 1− 1 q ⎜⎜⎝ 1 ∫ 0 |λΛ1(τ, 1) − Λ1(τ, ξ)| ||F′ (ξτ + (1 − ξ) ρ2)||qdξ⎟⎟⎠ 1 q”