Ostrowski Type Research Articles

Some new Ostrowski type fractional integral inequalities for generalized relative semi-(r; m, h)-preinvex mappings via Caputo k -fractional derivatives

In the present paper, the notion of generalized relative semi-(r; m, h)-preinvex mappings is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving generalized relative semi-(r; m, h)-preinvex mappings are given.Moreover, some new generalizations of Ostrowski type integral inequalities to generalized relative semi-(r; m, h)-preinvex mappings that are (n + 1)-differentiable via Caputo k-fractional derivatives are established. Some applications to special means are also obtain. It is pointed out that some new special cases can be deduced from main results of the article.

Some Refinements of Ostrowski’s Inequality and an Extension to a 2-Inner Product Space

The purpose of this paper is to prove certain refinements of Ostrowski’s inequality in an inner product space. We study extensions of Ostrowski type inequalities in a 2-inner product space. Finally, some applications which are related to the Chebyshev function and the Grüss inequality are presented.

On some k-fractional integral inequalities of~Hermite--Hadamard type for twice differentiable generalized beta (r, g)-preinvex functions

Abstract In the present paper, a new class of generalized beta ( r , g ) {(r,g)} -preinvex functions is introduced and some new integral inequalities for the left-hand side of Gauss–Jacobi type quadrature formula involving generalized beta ( r , g ) {(r,g)} -preinvex functions are given. Moreover, some generalizations of Hermite–Hadamard type inequalities for generalized beta ( r , g ) {(r,g)} -preinvex functions that are twice differentiable via k-fractional integrals are established. These general inequalities give us some new estimates for Hermite–Hadamard type k-fractional integral inequalities and also extend some results appeared in the literature; see [A. Kashuri and R. Liko, Ostrowski type fractional integral inequalities for generalized ( s , m , φ ) (s,m,\varphi) -preinvex functions, Aust. J. Math. Anal. Appl. 13 2016, 1, Article ID 16]. At the end, some applications to special means are given.

Fractional Ostrowski type inequalities for functions whose certain power of modulus of the first derivatives are pre-quasi-invex via power mean inequality

Abstract In this paper, we establish fractional Ostrowski’s inequalities for functions whose certain power of modulus of the first derivatives are pre-quasi-invex via power mean inequality.

New fractional Ostrowski type inequalities

In this work we obtain some new generalized fractional Montgomery identities for Katugampola fractional integral operator. Then, using these identities, we establish some new Ostrowski type inequalities.

New inequalities for $n$-time differentiable functions

In this paper, we obtain several inequalities of Ostrowski type that the absolute values of n-time differentiable functions are convex. Also, some applications to special means of real numbers are provided.

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

In this paper, we provide some Ostrowski type integral inequalities for functions whose derivatives in absolute value at some powers are strongly $(\alpha,m)$-convex with modulus $\mu\geq0$ via the $k$-Riemann-Liouvile fractional integral. Similar results related to $(\alpha,m)$-convex functions are obtained as a particular case.

Inequality of Ostrowski Type for Mappings with Bounded Fourth Order Partial Derivatives

A general Ostrowski’s type inequality for double integrals is given. We utilize function whose partial derivative of order four exists and is bounded.

Generalizations of Steffensen’s inequality by Lidstone’s polynomial and related results

In this paper we obtain few valuable identities by using Lidstone’s polynomial. Further, the identities were applied for constructing new generalizations of Steffensen’s inequality, namely for (2n)−convex and (2n + 1)−convex functions. In addition, using Čebyšev and Grüss type inequalities we consider the bounds for the integrals in the perturben versions of the previously described identities. Moreover, related Ostrowski type inequalities are given.

Generalized Canavati type g-fractional Iyengar and Ostrowski type

We present here generalized Canavati type g-fractional Iyengar and Ostrowski type inequalities. Our inequalities are with respect to all Lp norms: 1 ≤ p ≤ ∞. We finish with applications.

Ostrowski Type Inequality Using Five Step Weighted Kernel

The purpose of this paper is to establish weighted version of Ostrowski type integral inequalities. The inequalities are obtained by using a newly developed special type of five steps weighted kernel. The introduction of this new Kernel gives some new error bounds for various quadrature rules. Applications for Cumulative Distributive Functions are considered.

Fractional Ostrowski type inequalities for functions whose derivatives are s-preinvex

In this paper, some new fractional Ostrowski's inequalities for functions whose first derivatives in absolute value are $MT$-preinvex are established, mid point inequalities are also derived.

Ostrowski type inequalities via new fractional conformable integrals

In this present study, firstly, some necessary definitions and some results related to Riemann-Liouville fractional and new fractional conformable integral operators defined by Jarad et al. [ 13 ] are given. As a second, a new identity has been proved. By using this identity, new Ostrowski type inequalities has obtained involving fractional conformable integral operators. Also, some new inequalities has established for AG-convex functions via fractional conformable integrals in this study. Relevant connections of the results presented here with those earlier ones are also pointed out.

The Ostrowski type inequalities with the application to the three point integral formula

The Ostrowski type inequalities with the application to the three point integral formula

Generalization of weighted Ostrowski type inequalities by Abel-Gontscharoff polynomial

Generalization of weighted Ostrowski type inequalities by Abel-Gontscharoff polynomial

Weighted Ostrowski type inequalities by Lidstone polynomials

Weighted Ostrowski type inequalities by Lidstone polynomials

Generalization of weighted Ostrowski inequality with applications in numerical integration

An integral inequality of Ostrowski type with weights is established for differentiable functions up to second order, whose second derivatives are bounded and first derivatives are absolutely continuous. The inequality of weighted integral is then functional to weighted composite quadrature rules.

New Ostrowski and Ostrowski-Gruss type inequalities for double integrals on time scales involving a combination of $\Delta$-integral means

In 2014, some Ostrowski type inequalities for functions of a single variable were obtained in [Y. Jiang, H. R\"uzgar, W. J. Liu and A. Tuna: Some new generalizations of Ostrowski type inequalities on time scales involving combination of $\Delta$-integral means, J. Nonlinear Sci. Appl., {\bf{7}} (2014), 311--324]. In this paper, we extend some of the inequalities obtained in the above paper for double integrals. One of our results generalizes a result in the article [W. J. Liu, Q. A. Ng\^o and W. Chen: On new Ostrowski type inequalities for double integrals on time scales, Dyn. Syst. Appl., {\bf 19} (2010), 189--198]. We also apply our results to the continuous, discrete and quantum time scales to obtain some interesting inequalities.

Ostrowski-type fractional integral inequalities for mappings whose derivatives are h-convex via Katugampola fractional integrals

In this paper we generalize some Riemann-Liouville fractional integral inequalities of Ostrowski type for h-convex functions via Katugampola fractional integrals, generalization of Riemann- Liouville and the Hadamard fractional integrals. Also we deduce some known results by using p-functions, convex functions and s-convex functions.

A New Generalization of Ostrowski Type Inequalities for Mappings of Bounded Variation

In this paper, a new generalization of Ostrowski type integral inequality for mappings of bounded variation is obtained and the quadrature formula is also provided.