On Ostrowski type inequalities

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.

On generalizations related to the left side of Fejer's inequality via fractional integral operator

“…Motivated by results works done in [1,9,11], in this paper we show that Fejér type inequalities containing the Reimann-Liouville fractional integral operator and given in [11] can be extended to fractional integral operator introduced in [1,9].…”

“…With the help of (1.3), Raina [9] and Agarwal et al [1] defined the following left-sided and right-sided fractional integral operators respectively, as follows:…”

Generalized fractional Hermite-Hadamard type inequalities for m-convex and (α, m)-convex functions

“…With the help of (1.6), Raina [12] and Agarwal et al [1] de…ned the following left-sided and right-sided fractional integral operators respectively, as follows:…”

Hermite-Hadamard Type Inequalities for convex functions via generalized fractional integral operators

“…In [2], Raina introduced a class of functions de ned formally by x k (ρ, λ > ; |x| < R), (1.2) where the coe cients σ(k) (k ∈ N = N ∪ { }) is a bounded sequence of positive real numbers and R is the set of real numbers. With the help of (1.2), Raina and Agarwal et al [1] de ned the following left-sided and right-sided fractional integral operators respectively, as follows:…”

“…For instance the classical Riemann-Liouville fractional integrals J α a+ and J α b− of order α follow easily by setting λ = α, σ( ) = and w = in (1.3) and (1.4). To see more results and details on fractional integral operators see ( [1], [2], [5], [9][10][11][12][13][14] …”